Fracture criteria for combined cleavage and dislocation emission

A general theory of fracture criteria for mixed dislocation emission and cleavage processes is developed based on Ohr's model. Complicated cases involving mixed-mode loading are considered. Explicit formulae are proposed for the critical condition of crack cleavage propagation after a number of dislocation emissions. The effects of crystal orientation, crack geometry and load phase angle on the apparent critical energy release rates and the total number of the emitted dislocations at the initiation of cleavage are analysed in detail. In order to evaluate the effects of nonlinear interaction between the slip displacement and the normal separation, an analysis of fracture criteria for combined dislocation emission and cleavage is presented on the basis of the Peierls framework. The calculation clearly shows that the nonlinear theory gives slightly high values of the critical apparent energy release rate G(c) for the same load phase angle. The total number N of the emitted dislocations at the onset of cleavage given by nonlinear theory is larger than that of linear theory.

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).

Mesofracture mechanics: a necessary link

Classical fracture mechanics is based on the premise that small scale features could be averaged to give a larger scale property such that the assumption of material homogeneity would hold. Involvement of the material microstructure, however, necessitates different characteristic lengths for describing different geometric features. Macroscopic parameters could not be freely exchanged with those at the microscopic scale level. Such a practice could cause misinterpretation of test data. Ambiguities arising from the lack of a more precise range of limitations for the definitions of physical parameters are discussed in connection with material length scales. Physical events overlooked between the macroscopic and microscopic scale could be the link that is needed to bridge the gap. The classical models for the creation of free surface for a liquid and solid are oversimplified. They consider only the translational motion of individual atoms. Movements of groups or clusters of molecules deserve attention. Multiscale cracking behavior also requires the distinction of material damage involving at least two different scales in a single simulation. In this connection, special attention should be given to the use of asymptotic solution in contrast to the full field solution when applying fracture criteria. The former may leave out detail features that would have otherwise been included by the latter. Illustrations are provided for predicting the crack initiation sites of piezoceramics. No definite conclusions can be drawn from the atomistic simulation models such as those used in molecular dynamics until the non-equilibrium boundary conditions can be better understood. The specification of strain rates and temperatures should be synchronized as the specimen size is reduced to microns. Many of the results obtained at the atomic scale should be first identified with those at the mesoscale before they are assumed to be connected with macroscopic observations. Hopefully, "mesofracture mechanics" could serve as the link to bring macrofracture mechanics closer to microfracture mechanics.

Dynamic failure in ductile porous materials

In this paper, a mathematical model of dynamic fracture in porous ductile materials under intense dynamic general loading is developed. The mathematical model includes the influence of inertial effects and material rate sensitivity, as well as the contribution of surface energy of a void and material work-hardening. In addition, the condition of the void compaction is considered as well. The threshold stresses for the void growth and compaction are obtained. A simple criterion for ductile fracture which is associated with material distention and plastic deformation is adopted. As an application of the theoretical model, the processes of two-dimensional spallation in LY12 aluminum alloy are successfully simulated by means of two-dimensional finite-difference Lagrangian code.

Experimental-study on the criteria and mechanism of spallation in an aluminum-alloy

In this paper, a damage function defined by the residual strength of spalled specimens of an aluminium alloy is given to characterize the spallation of the material. Based on this function a simple method for continuously describing the spallation may be developed. Stress wave profiles showing the signal of spallation were successfully obtained with carbon gauges. Microscopic observations of the spalled aluminium alloy specimens reveal that the nucleation of spallation initiates from cracking of the second phase particles. Spallation is a process of crack nucleation, growth and coalescence to final, complete disintegration.

Extending Tsai-Hill and norris criteria to predict cracking direction in orthotropic materials

methods of lifetime measurement are discussed.

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 D-2, 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 D-2 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 D-2 is also constant along the crack faces and the electric field E-2 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.

Dislocation theory of the fracture criterion for anisotropic solids

A dislocation theory of fracture criterion for the mixed dislocation emission and cleavage process in an anisotropic solid is developed in this paper. The complicated cases involving mixed-mode loading are considered here. The explicit formula for dislocations interaction with a semi-infinite crack is obtained. The governing equation for the critical condition of crack cleavage in an anisotropic solid after a number dislocation emissions is established. The effects of elastic anisotropy, crack geometry and load phase angle on the critical energy release rate and the total number of the emitted dislocations at the onset of cleavage are analysed in detail. The analyses revealed that the critical energy release rates can increase to one or two magnitudes larger than the surface energy because of the dislocation emission. It is also found elastic anisotropy and crystal orientation have significant effects on the critical energy release rates. The anisotropic values can be several times the isotropic value in one crack orientation. The values may be as much as 40% less than the isotropic value in another crack orientation and another anisotropy parameter. Then the theory is applied to a fee single crystal. An edge dislocation can emit from the crack tip along the most highly shear stressed slip plane. Crack cleavage can occur along the most highly stressed slip plane after a number of dislocation emissions. Calculation is carried out step by step. Each step we should judge by which slip system is the most highly shear stressed slip system and which slip system has the largest energy release rate. The calculation clearly shows that the crack orientation and the load phase angle have significant effects on the crystal brittle-ductile behaviours.

Micro-Fracture Toughness in a Nanoceramic Composite

Micro-fracture toughness in one nanoceramic composite, Al_2O_3/SiC_{nano}, is measured by Nanoindentation tests. Microscopy is adopted to probe that all nanoindentations are local at Al_2O_3, matrix component of the current composite and measure length of radial micro-cracks at corriers of nanoindentation. The measured fracture toughness at the shallow indentation is higher than those at deeper ones. Relations between micro-toughness and peak loads as well as peak depths are discussed. And an analysis to the energy consumed during the indentation and fracture toughness explained that, the lower fracture toughness measured in the deeper impression probably resulted from its fracture modes yielded by higher load and larger depth.

Numerical Analysis of Rainfall Infiltration in the Slope with a Fracture

With the finite volume method, a 2D numerical model for seepage in unsaturated soil has been established to study the rainfall infiltration in the fractured slope.The result shows that more rain may infiltrate into the slope due to existing fracture and then the pore pressure rises correspondingly. Very probably, it is one of the crucial factors accounting for slope failure. Furthermore a preliminary study has been conducted to investigate the influence of various fracture and rainfall factors such as the depth, width and location of a crack, surface condition, rainfall intensity and duration. Pore pressure and water volumetric content during the transient seepage are carefully examined to reveal the intrinsic mechanism.

A new model for the energy release rate of fibre/matrix interfacial fracture

On the basis of the well-known shear-lag analysis of fibre/matrix interface stresses and the assumption of identical axial strains in the fibre and matrix, a new model for predicting the energy release rate of interfacial fracture of the fibre pull-out test model is attempted. The expressions for stresses in the fibre, matrix and interface are derived. The formula for interfacial debonding energy release rate is given. Numerical calculations are conducted and the results obtained are compared with those of the existing models.

Investigation of Dynamic Fracture Toughness under Compressive-Shear Combinede Stress Wave Loading

提出亚微秒单脉冲应力波载荷作用下II型裂纹的平板冲击实验技术。加载率为dK/dt-10~8MPa·m~{”/d}·s~{-1}。实验中由锰铜应力片和弹性波理论分别测定和计算了压应力；通过微观分析确定了动态裂纹的平均扩展长度；引进等效应力强度因子,用动态断裂理论确定了60号钢的动态断裂韧性K_{Id}和K_{IId}；建立了亚微秒冲击载荷作用下确定材料动态断裂韧性的方法。

Static Shape Control Employing Displacement-Stress Dual Criteria

An approach employing displacement-stress dual criteria for static shape control is presented. This approach is based on normal displacement control, and stress modification is considered in the whole optimization process to control high stress in the local domain. Analysis results show that not only is the stress reduced but al so that the controlled surface becomes smoother than before.

A micromechanical damage theory for brittle materials with small cracks

For brittle solids containing numerous small cracks, a micromechanical damage theory is presented which accounts for the interactions between different small cracks and the effect of the boundary of a finite solid, and includes growth of the pre-existing small cracks. The analysis is based on a superposition scheme and series expansions of the complex potentials. The small crack evolution process is simulated through the use of fracture mechanics incorporating appropriate failure criteria. The stress-strain relations are obtained from the micromechanics analysis. Typical examples are given to illustrate the potential capability of the proposed theory. These results show that the present method provides a direct and efficient approach to deal with brittle finite solids containing multiple small cracks. The stress-strain relation curves are evaluated for a rectangular plate containing small cracks.

Two critical crack propagating velocities for PMMA fracture surface

Ultrasonic fractography and scanning electronic microscopy (SEM) are used to determine the direct relationship between the fracture surface morphology and the main crack velocity during the rapid rupture of polymethylmethacrylate (PMMA). Two critical crack velocities are found for the fracture. Quasi-parabolic markings will appear when the crack speed exceeds the first critical speed. Crack propagating at speed above the second critical speed leaves a thicket of small branches penetrating the surface behind them. Both critical speeds are functions of the thickness of the specimens.