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.

Microdamage Evolution, Energy Dissipation and Their Trans-Scale Effects on Macroscopic Failure

The process of damage evolution concerns various scales, from micro- to macroscopic. How to characterize the trans-scale nature of the process is on the challenging frontiers of solid mechanics. In this paper, a closed trans-scale formulation of damage evolution based on statistical microdamage mechanics is presented. As a case study, the damage evolution in spallation is analyzed with the formulation. Scaling of the formulation reveals that the following dimensionless numbers: reduced Mach number M, damage number S, stress wave Fourier number P, intrinsic Deborah number D*, and the imposed Deborah number De*, govern the whole process of deformation and damage evolution. The evaluation of P and the estimation of temperature increase show that the energy equation can be ignored as the first approximation in the case of spallation. Hence, apart from the two conventional macroscopic parameters: the reduced Mach number M and damage number S, the damage evolution in spallation is mainly governed by two microdamage-relevant parameters: the Deborah numbers D* and De*. Higher nucleation and growth rates of microdamage accelerate damage evolution, and result in higher damage in the target plate. In addition, the mere variation in nucleation rate does not change the spatial distribution of damage or form localized rupture, while the increase of microdamage growth rate localizes the damage distribution in the target plate, which can be characterized by the imposed Deborah number De*.

Statistical and stochastic description of microvoid evolution observed in dynamic failure of ductile materials

A brief review is presented of statistical approaches on microdamage evolution. An experimental study of statistical microdamage evolution in two ductile materials under dynamic loading is carried out. The observation indicates that there are large differences in size and distribution of microvoids between these two materials. With this phenomenon in mind, kinetic equations governing the nucleation and growth of microvoids in nonlinear rate-dependent materials are combined with the balance law of void number to establish statistical differential equations that describe the evolution of microvoids' number density. The theoretical solution provides a reasonable explanation of the experimentally observed phenomenon. The effects of stochastic fluctuation which is influenced by the inhomogeneous microscopic structure of materials are subsequently examined (i.e. stochastic growth model). Based on the stochastic differential equation, a Fokker-Planck equation which governs the evolution of the transition probability is derived. The analytical solution for the transition probability is then obtained and the effects of stochastic fluctuation is discussed. The statistical and stochastic analyses may provide effective approaches to reveal the physics of damage evolution and dynamic failure process in ductile materials.

Failure process analysis of cement under explosive loading with a generalized driven nonlinear threshold model

The microstructural heterogeneity and stress fluctuation play important roles in the failure process of brittle materials. In this paper, a generalized driven nonlinear threshold model with stress fluctuation is presented to study the effects of microstructural heterogeneity on continuum damage evolution. As an illustration, the failure process of cement material under explosive loading is analyzed using the model. The result agrees well with the experimental one, which proves the efficiency of the model.

Elastic and statistically brittle (ESB) model, damage localization and catastrophic rupture

In this paper, an elastic and statistically brittle (ESB) model is applied to the process of damage evolution induced catastrophic rupture and the influence of localization and softening on catastrophic rupture is discussed. According to the analysis, the uncertainty of catastrophic rupture should be attributed to the unknown scale of localized zone. Based on the elastic and statistically brittle model but local mean field approximation, the relation between the scale of localized zone and catastrophic rupture is obtained and then justified with experiments. These results can not only give a deeper understanding of the mechanism governing catastrophic rupture, but also provide a possible tool to foresee the occurrence of catastrophic rupture.

The development of an inhomogeneous damage field in an elastic-plastic model

By making use of the evolution equation of the damage field as derived from the statistical mesoscopic damage theory, we have preliminarily examined the inhomogeneous damage field in an elastic-plastic model under constant-velocity tension. Three types of deformation and damage field evolution are presented. The influence of the plastic matrix is examined. It seems that matrix plasticity may defer the failure due to damage evolution. A criterion for damage localization is consistent with the numerical results.

Catastrophic Rupture Induced Damage Coalescence in Heterogeneous Brittle Media

In heterogeneous brittle media, the evolution of damage is strongly influenced by the multiscale coupling effect. To better understand this effect, we perform a detailed investigation of the damage evolution, with particular attention focused on the catastrophe transition. We use an adaptive multiscale finite-element model (MFEM) to simulate the damage evolution and the catastrophic failure of heterogeneous brittle media. Both plane stress and plane strain cases are investigated for a heterogeneous medium whose initial shear strength follows the Weibull distribution. Damage is induced through the application of the Coulomb failure criterion to each element, and the element mesh is refined where the failure criterion is met. We found that as damage accumulates, there is a stronger and stronger nonlinear increase in stress and the stress redistribution distance. The coupling of the dynamic stress redistribution and the heterogeneity at different scales result in an inverse cascade of damage cluster size, which represents rapid coalescence of damage at the catastrophe transition.

Dynamic function of damage and its implications

Dynamic function of damage is the key to the problem of damage evolution of solids. In order to understand it, one must understand its mesoscopic mechanisms and macroscopic formulation. In terms of evolution equation of microdamage and damage moment, a dynamic function of damage is strictly defined. The mesoscopic mechanism underlying self-closed damage evolution law is investigated by means of double damage moments. Numerical results of damage evolution demonstrate some common features for various microdamage dynamics. Then, the dynamic function of damage is applied to inhomogeneous damage field. In this case, damage evolution rate is no longer equal to the dynamic function of damage. It is found that the criterion for damage localization is closely related to compound damage. Finally, an inversion of damage evolution to the dynamic function of damage is proposed.

A Nonlinear Threshold Model Applied to Spallation Analysis

Spallation in heterogeneous media is a complex, dynamic process. Generally speaking, the spallation process is relevant to multiple scales and the diversity and coupling of physics at different scales present two fundamental difficulties for spallation modeling and simulation. More importantly, these difficulties can be greatly enhanced by the disordered heterogeneity on multi-scales. In this paper, a driven nonlinear threshold model for damage evolution in heterogeneous materials is presented and a trans-scale formulation of damage evolution is obtained. The damage evolution in spallation is analyzed with the formulation. Scaling of the formulation reveals that some dimensionless numbers govern the whole process of deformation and damage evolution. The effects of heterogeneity in terms of Weibull modulus on damage evolution in spallation process are also investigated.

Collective evolution characteristics and computer simulation of short fatigue cracks

Fatigue testing was conducted using a kind of triangular isostress specimen to obtain the short-fatigue-crack behaviour of a weld low-carbon steel. The experimental results show that short cracks continuously initiate at slip bands within ferrite grain domains and the crack number per unit area gradually increases with increasing number of fatigue cycles. The dispersed short cracks possess an orientation preference, which is associated with the crystalline orientation of the relevant slip system. Based on the observed collective characteristics, computer modelling was carried out to simulate the evolution process of initiation, propagation and coalescence of short cracks. The simulation provides progressive displays which imitate the appearance of experimental observations. The results of simulation indicate that the crack path possesses a stable value of fractal dimension whereas the critical value of percolation covers a wide datum band, suggesting that the collective evolution process of short cracks is sensitive to the pattern of crack site distribution.

Experimental and theoretical study on numerical density evolution of short fatigue cracks

Fatigue testing was performed using a kind of triangular shaped specimen to obtain the characteristics of numerical density evolution for short cracks at the primary stage of fatigue damage. The material concerned is a structural alloy steel. The experimental results show that the numerical density of short cracks reaches the maximum value when crack length is slightly less than the average grain diameter, indicating grain boundary is the main barrier for short crack extension. Based on the experimental observations and related theory, the expressions for growth velocity and nucleation rate of short cracks have been proposed. With the solution to phase space conservation equation, the theoretical results of numerical density evolution for short cracks were obtained, which were in agreement with our experimental measurements.

Numerical simulation of evolution-induced catastrophe

A numerical simulation of damage evolution in a two-dimensional system of micocracks is presented. It reveals that the failure is induced by a cascade of coalescences of microcracks, and the fracture surface appears fractal. A model of evolution-induced catastrophe is introduced. The fractal dimension is found to be a function of evolution rule only. This result could qualitatively explain the correlation of fractal dimension and fracture toughness discovered in experiments.

Catastrophic Rupture Induced Damage Coalescence in Heterogeneous Brittle Media

In heterogeneous brittle media, the evolution of damage is strongly influenced by the multiscale coupling effect. To better understand this effect, we perform a detailed investigation of the damage evolution, with particular attention focused on the catastrophe transition. We use an adaptive multiscale finite-element model (MFEM) to simulate the damage evolution and the catastrophic failure of heterogeneous brittle media. Both plane stress and plane strain cases are investigated for a heterogeneous medium whose initial shear strength follows the Weibull distribution. Damage is induced through the application of the Coulomb failure criterion to each element, and the element mesh is refined where the failure criterion is met. We found that as damage accumulates, there is a stronger and stronger nonlinear increase in stress and the stress redistribution distance. The coupling of the dynamic stress redistribution and the heterogeneity at different scales result in an inverse cascade of damage cluster size, which represents rapid coalescence of damage at the catastrophe transition.

Influence of the AlN interlayer crystal quality on the strain evolution of GaN layer grown on Si (111)

The strain evolution in metal organic chemical vapor deposition growth of GaN on Si (111) substrate with an AlN interlayer is studied. During the growth of GaN film on AlN interlayer, the growth stress changes from compression to tension. The study shows that the density of V trenches in the AlN interlayer surface and the threading dislocations generated in the AlN interlayer have a significant influence on this strain evolution process. The dislocations generated in AlN interlayer may thread across the interface and play a key role in the strain evolution process of the GaN layer grown on AlN interlayer.

Excitation energy distribution between two photosystems in Porphyra yezoensis and its significance in photosynthesis evolution

Comparative investigation on energy distribution between two photosystems were carried out in the sporophytes and gametophytes of Porphyra yezoensis. By performing 77 K fluorescence spectra, we suggested that there probably existed a pathway for energy transfer from PS II to PS I to redistribute the absorbed energy in gametophytes, while no such a way or at minor level in sporophytes. Electron transfer inhibitor DCMU blocked the energy transfer from PS II to PS I in gametophytes, but no obvious effects on sporophytes. These indicated that excitation energy distribution between two photosystems in gametophytes was more cooperative than that in sporophytes. These data in ontogenesis reflected the evolution process of photosynthetic organisms and supported the hypothesis of independent evolution of each photosystem.