Zhonghua Li

Crack¿inclusion interaction for mode II crack analyzed by Eshelby equivalent inclusion method

Several simple formulas have been developed to predict the variations of stress intensity factors for mode I crack induced by the stiffness and geometry of the near crack-tip inclusion. The derivation of the fundamental formula is based on the transformation toughening theory. The unconstrained mismatch strains between matrix and inclusion, which induce the variation of the near crack-tip field, are estimated based on the Eshelby equivalent inclusion approach. As validated by numerical examples, the developed formulas have satisfactory accuracy for a wide range of the modulus ratio between inclusion and matrix as long as the inclusion is located in the K0-controlled field.

The Near-Tip Stress Intensity Factor for a Crack Partially Penetrating an Inclusion

When a crack is lodged in an inclusion, the difference between the elastic modulus of the inclusion and matrix material will cause the near-tip stress intensity factor to be greater or less than that prevailing in a homogeneous material. A method is derived for calculation of the near-tip stress intensity factor for the inclusion with arbitrary shape. The derivation of the fundamental formula is based on the transformation toughening theory. The equivalent transformation strain contributed from modulus difference between inclusion and matrix is calculated from Eshelby equivalent inclusion approach. As validated by numerical examples, the developed formula has excellent accuracy.

Electromigration-induced Coble creep in polycrystalline materials

A simple expression has been derived for the prediction of the creep rate controlled by electromigration-induced grain boundary diffusion. The creep rate depends linearly on the current density and the grain boundary diffusivity, and inversely on grain size squared. It is also demonstrated that the electromigration-induced creep can be fully suppressed by a critical compressive stress gradient.

The application of the Eshelby equivalent inclusion method for unifying modulus and transformation toughening

When a crack is lodged in an inclusion, both difference between the modulus of the inclusion and matrix material and stress-free transformation strain of the inclusion will cause the near-tip stress intensity factor to be greater (amplification effect) or less (shielding or toughening effect) than that prevailing in a homogeneous material. In this paper, the inclusion may represent a second phase particle in composites and a transformation or microcracked process zone in brittle materials, which may undergo a stress-free transformation strain induced by phase transformation, microcracking, thermal expansion mismatch and so forth. A close form of solution is derived for predicting the toughening (or amplification) effect. The derivation is based on Eshelby equivalent inclusion approach that provides rigorous theoretical basis to unify the modulus and transformation contributions to the near-tip field. As validated by numerical examples, the developed formula has excellent accuracy for different application cases.

Finite element analysis of the splitting and cylinderization processes of damage microcracks

A two-dimensional finite element method is applied to analyse the splitting and cylinderization processes of a damage microcrack during healing. These processes are controlled by surface diffusion. The cross section of the damage microcrack is assumed to be an ellipsoid and its aspect ratio is defined by the ratio of the major axis to the minor axis. Two models of microcrack splitting are developed, namely a high-aspect ratio model and a grain-boundary grooving model. The splitting processes based on the two models are simulated. A critical aspect ratio is predicted, below which the microcrack will directly evolve into a cylindrical pore channel if there is no other energetic mechanism to split the crack and above which two or more cylindrical pore channels will be formed. Grain boundary grooving may split a microcrack when the crack aspect ratio is larger than a threshold value. The value of the threshold is predicted for a grain boundary perpendicular to the centre of crack surface. An approximate formula is given for predicting the critical grain boundary energy, at which the microcrack can be split, as a function of microcrack aspect ratio.

Some simple formulas to predict the variation of stress intensity factors for mode I crack induced by near crack-tip inclusion

Abstract Several simple formulas have been developed to predict the variations of stress intensity factors (SIFs) for mode I crack induced by the inclusion within crack-tip field. The derivation of the fundamental formula is based on the transformation toughening theory. The unconstrained mismatch strains between matrix and inclusion, which induce the variation of the near crack-tip field, are estimated from the remote applied SIF K0. As validated by numerical examples, the developed formulas have satisfactory accuracy for wide range of the modulus ratios between inclusion and matrix as long as the inclusion is located in the K0-controlled field.

Effects of stress and temperature gradients on the evolution of void in metal interconnects driven by electric current and mechanical stress

The effects of the electromigration-induced stress gradient and temperature gradient on the void evolution in interconnect are examined by numerical simulation. It is found that the void in a stress gradient field will move to higher stress zone, regardless of tensile stress or compressive stress. The void motion driven by electromigration will be retarded by compressive stress gradient and accelerated by tensile stress gradient. The stress gradient has the effect of elongating the void along the interconnect line, shorting its size in line width. Hence, it may delay the open failure of the interconnect line. The temperature gradients due to current crowding cause local changes in resistivity and diffusivity in the vicinity of the evolving void, leading to void motion more rapidly along the interconnect line and void growth in the line width. Thus, the temperature gradient around the void tends to accelerate the open failure process of the interconnect.

Evolution of penny-shaped microcracks by interface migration

An axisymmetric finite element method is developed and employed to simulate healing evolution of intragranular penny-shaped microcracks under interface migration driven by total free energy change consisted of surface tension and chemical potential difference between phases. The validity of the method is confirmed by an agreement of the shrinkage and growth behavior, simulated numerically, of an isolated spherical grain with those predicted theoretically. The results showed that the surface tension alone serves to evolve the initial penny shape to a spherical one and, coupled with the chemical potential difference, dominates volume shrinkage of the microcracks. As the initial aspect ratio of a microcrack increases, both spheroidization and volume shrinkage times increase continuously. And the volume shrinkage process of the microcracks can be greatly promoted with an increase in the chemical potential difference.

Engineering treatment model for creep crack driving force estimation: CTOD in terms of δ5

Abstract Based on finite element analyses, a set of formulas for estimating the crack driving force under creep conditions in terms of the crack tip opening displacement (CTOD), δ 5 , which measures the CTOD at the specimen side surface, spanning the original crack tip over a gauge length of 5 mm, is presented for three fracture specimens. These formulas are developed for stationary and growing cracks for both plane stress and plane strain conditions, validated for different creep laws and loading conditions. These formulas are in closed form and accurately replicate finite element results. The creep δ 5 is a promising load parameter for creep ductile materials. The calculation of the creep δ 5 and the creep fracture analysis based on the creep δ 5 -concept are very convenient. They can be done by use of the nominal net section stress defined by the limit load of the cracked body and the original uniaxial creep curve at the corresponding net section stress level.

The Effect of a Plastically Deformed Zone Near Crack Tip on the Stress Intensity Factors

A plastically deformed particle ahead of a crack-tip is treated as an equivalent transformation inclusion by means of Eshelby equivalent inclusion theory. A general solution to determine the effect of the plastically deformed particle on the stress intensity factor of mode I crack is obtained.