Elliptical Microcracks Research Articles

Constitutive model of multiphase ceramics based on microcrack damage evolution

abstract The damage evolution of microcracks that dispersed in eutectic composite ceramics is an important factor leading to fracture failure. We propose a meso damage model (CMMC), which uses our proposed two-scale cellular model with microcracks, and fully considers the characteristics of the microstructure on the eutectic composite ceramics, thus providing a more objective structural modeling. In addition, there are two significant features existing in CMMC: One is to use the interaction direct derivative (IDD) estimate method to calculate the additional flexibility increment caused by a single open elliptical microcrack, which considers the spatial orientation of the microcrack. The other is that the additional flexibility tensor from the microcrack system is obtained by introducing probability density function and selecting appropriate microcrack growth criteria. Experiments on the related datasets show that CMMC achieves the consistent results compared with the experimental data. Furthermore, the effects of microcrack aspect ratio and microstructure parameters on the effective properties of multiphase ceramics were analyzed by using numerical method. • Damage evolution of microcracks in composite ceramics leading to fracture failure. • A meso damage model based on microcrack damage evolution is proposed. • Microcrack aspect ratio affects effective properties of multiphase ceramics. • Microstructure parameters influences effective properties of multiphase ceramics. • The additional flexibility tensor from the microcrack system is obtained.

Probabilistic micromechanical damage model for mixed mode I/II fracture investigation of composite materials

The non-linear behavior of cracked body composite materials can originate from toughening mechanisms in the crack-tip damage zone. Given the damage zone complexity, the residual strength and overall compliance of micro-crack-weakened solid are used for characterization by a micromechanical damage approach. In the present research, a mixed mode I/II criterion called “damage zone micro-mechanical criterion” is presented for composite materials. In this context, a semi-empirical image processing method and relative probabilistic functions are employed to characterize the moment of crack propagation based on the dispersion of orientated elliptical micro-cracks. In addition, it is assumed that the micro-crack growth occurs in isotropic matrix where fibers play as reinforcement of the matrix by utilizing stress reduction coefficients. In this research, a remarkable precision is obtained considering micromechanical criterion in comparison with experimental data.

Discrete crack dynamics: A planar model of crack propagation and crack-inclusion interactions in brittle materials

The Multipole Method (MPM) is used to simulate the many-body self-consistent problem of interacting elliptical micro-cracks and inclusions in single crystals. A criterion is employed to determine the crack propagation path based on the stress distribution; the evolution of individual micro-cracks and their interactions with existing cracks and inclusions is then predicted using what we coin the Discrete Crack Dynamics (DCD) method. DCD is fast (semi-analytical) and particularly suitable for the simulation of evolving low-speed crack networks in brittle or quasi-brittle materials. The method is validated against finite element analysis predictions and previously published experimental data.

Micromechanics model of gas saturated coal weakened by elliptical microcracks

Based on the analysis of the deformation and growth of a representative elliptical microcrack with arbitrary orientation and geometrical size embedded in a representative volume element subjected to triaxial stress and pore pressure, the additional compliance tensor induced by an embedded opening/closed elliptical microcrack is derived. Assuming numerous elliptical microcracks, and introducing an appropriate probability density function to describe the distribution of orientation and geometrical size of microcracks, the additional compliance tensor induced by microcracks system is analyzed in Taylor’s scheme, and a three-dimensional micromechanics model for gas saturated coal materials is obtained. The validity of the proposed micromechanics model is verified by the agreement between the theoretical and experimental results of gas saturated coal under triaxial compression. The effect of pore pressure and confining pressure on the damage behavior induced by microcracks is investigated. The calculations show microcracks of coal under higher pore pressure will be more inclined to slide and grow, and induce larger additional strain in the last deformation stage.

Effects of the microcrack shape, size and direction on the poroelastic behaviors of a single osteon: a finite element study.

In this work, a finite element study is proposed by using the Comsol Multiphysics software to evaluate the effects of microcrack shape, size and direction on the poroelastic behaviors of a single osteon. This finite element model is established by using the Comsol Multiphysics software, and we just focus on the comparison of the influences of those microcrack geometric parameters on the osteonal fluid pressure and velocity. The results show that: (1) microcracks in the osteon wall can induce a release of the fluid pressure, but enlarge the velocity in this region; (2) equal-area microcrack with ellipsoid-like shape produced a larger fluid pressure and velocity fields in the osteon than that of rectangular shape; (3) in the elliptic microcracks, the longer of the length (major semi-axis) induces a smaller fluid pressure and velocity amplitudes, whereas the width (minor axis) has little effect; (4) the direction of the microcracks (major axial direction) has an limited influence area around about 1/15 of the osteon cross-sectional area. This model permits the linking of the external loads and microcracks to the osteonal fluid pressure and velocity, which can be used for other purpose associate microcracks with the mechanotransduction and bone remodeling.

Continuum Model of Deformation of Piezoelectric Materials with Cracks

The present paper addresses the continuum model describing deformation and accumulation of microdamages in electroelastic materials based on the generalized Eshelby principle. The microdamageability is considered as a process of appearance of flat elliptic or circular microcracks randomly dispersed over volume, the concentration of which increases with a load. The Eshelby method is based on the principle of equivalence of the deformation energy of fractured piezoelectric materials and the energy of medium, which is modeling these materials as a continuous medium. The key point of this approach is to determine the densities of the released elastic and electric energy.

Research on the process of micro-crack damage evolution and coalescence in brittle materials

Damage and failure of quasi-brittle materials are caused by evolution and coalescence of micro-cracks. To solve the problem of elliptical micro-crack growth at the elastic deformation stage, a method of complex potential functions is proposed and the effect of the initial orientation on micro-crack growth and deflection is discussed. The critical stress condition for the initial damage is derived according to the criterion of micro-crack growth. Based on energy conservation during wing-crack propagation, a damage constitutive model is developed with the strain criterion created in the condition of micro-crack coalescence. The stress–strain curves of quasi-brittle materials in uniaxial compression obtained based on this model are examined with the experimental results. In conclusion, (1) wing crack growth, propagation, and coalescence at the tips of micro-cracks eventually lead to the formation of an anisotropic effective compliance tensor in the damaged material; (2) a large number of micro-crack coalescence is a highly nonlinear phenomenon resulting in failure of materials; and (3) the effective elastic modulus of damaged material decreases with the wing crack propagation length increasing.

A constitutive model based on the evolution and coalescence of elliptical micro-cracks for quasi-brittle materials

Damage and failure of quasi-brittle materials are caused by the evolution and coalescence of micro-cracks. To solve the problem of elliptical micro-crack growth at the elastic deformation stage, a method of complex potential functions is proposed and the effect of the initial orientation on micro-crack growth and deflection is discussed. The critical stress condition for the initial damage is derived according to the criterion of micro-crack growth. Based on energy conservation during wing-crack propagation, a damage constitutive model is developed with the strain criterion created in the condition of micro-crack coalescence. The stress-strain curves of quasi-brittle materials in uniaxial compression obtained based on this model are examined with the experimental results.

Deformation of Damaged Elastic-Brittle Isotropic Materials with a Fixed Concentration of Microdefects in a Complex Stress State

The character of deformation of elastic—brittle isotropic materials weakened by flat microdefects in the form of circular or elliptic microcracks randomly dispersed over volume is studied in the complex stress state. It is assumed that concentration of the microcracks under loading remains constant. Equations of state for such materials are derived depending on the stress state mode and sign of applied stresses. The damaged material is simulated by a linear elastic isotropic medium under all-round compression or tension and under biaxial compression, by a linear elastic transversally isotropic medium under biaxial tension, and by a non-linear orthotropic medium under compression along one axis and tension along another axis. To determine compliance characteristics entering into the equations of state, the continual model of a cracked medium and a method based on the equivalence principle of deformation energy of this medium are used. A numerical example is presented.

A three-dimensional micromechanics model for the damage of brittle materials based on the growth and unilateral effect of elliptic microcracks

Abstract Based on the analysis of a representative elliptic microcrack embedded in a RVE, the additional compliance tensor induced by an embedded opening/closed microcrack is derived, and that corresponding to the kinked growth of a closed elliptic microcrack is also derived by making use of its approximately equivalent simplification. The effect of the microcracks is analyzed with the Taylor’s scheme by introducing an appropriate probability density function. A three-dimensional micromechanics damage model is obtained for brittle materials, assuming numerous randomly distributed elliptic microcracks and taking into account their deformation, frictional sliding, growth and kinked growth.

On dispersed microdamageability of elastic-brittle materials under deformation

The variant of a continuum model describing joint deformation and accumulation of microdamages in elastic-brittle materials is presented. The microdamageability is considered as the process of origin of a system of flat elliptic or circular microcracks randomly dispersed over volume, the concentration of which increases with a load. The damageable material is simulated by the continuous medium, for which the elastic symmetry and non-linear law of deformation are attributed to the pattern of the microstrength distribution, microfracture mechanism, and the mode of the stress state induced in the body. The model provided is used to describe the possible mechanism of non-linear deformation for practically all materials within the range of small strains.

A Consistent Anisotropic Brittle Damage Model Based on Growing Elliptical Microcracks

A Consistent Anisotropic Brittle Damage Model Based on Growing Elliptical Microcracks

Analysis of micro--macro material properties and mechanical effects of damaged material containing periodically distributed elliptical microcracks

The existence of numerous microcracks causes changes in the stiffness or fracture toughness of materials. In this paper, the manifestations of mechanical properties in the damaged materials caused by the microcracks are evaluated by the present homogenization method based on the superposition method together with the VNA solution. Moreover, it is known that the stress concentration at the macrocrack tip decreases due to the stress relaxation effect caused by the existence of the microcracks. In order to evaluate the manifestations of mechanical behavior, the mechanical effects of the existence of the microcracks on the macrocrack, the component separation method for mixed-mode stress intensity factors of the macrocrack in the damaged materials is newly developed in this paper. Various numerical analyses are successfully conducted for the two topics, the mechanical properties of the damaged materials and the mechanical behavior of the macrocrack in the damaged materials.

Analysis of damaged material containing periodically distributed elliptical microcracks by using the homogenization method based on the superposition method

The presence of multiple microcracks in a structural component causes material degradation such as reduction in the stiffness or reduction in the fracture toughness of the component. In this paper, the homogenization method is used to evaluate mechanical properties of the damaged material. The adaptation of the superposition method to the homogenization method is also presented. The proposed method makes use of the finite element solution of uncracked solid and the analytical solution. The effective elastic moduli of damaged materials containing lattice-distribution microcracks are estimated by the proposed method. Furthermore, the stress fields and the stress intensity factors of the elliptical microcracks in the damaged material at a micro-mechanics scale are evaluated to illustrate microscopic behavior such as crack interaction.

Representation of mechanical loads in molecular dynamics simulations

We describe a constant-traction molecular dynamics method to perform simulations of a generic atomistic system under an applied external load. The main objective is to ensure consistency between the atomistic model and the macroscopic continuum-mechanics description. Examples of simulations for different kinds of extended defects under an external load, such as a grain boundary, an elliptical microcrack, and a screw dislocation in a fcc crystal are presented, and compared with the results of the corresponding continuum mechanics description.

Effective Elastic Compliances and Engineering Constants for Damaged Isotropic Solids

In continuum damage mechanics, damaged solids have been represented by the effective elastic stiffness into which local damages are smoothly smeared. In parallel to the effective elastic stiffness representation, damaged solids may be represented in terms of effective elastic compliance. It then becomes easier to derive the effective engineering constants (i.e., effective elastic moduli and Poisson's ratios) for damaged solids, all in closed forms, from the effective elastic compliance rather than from the effective elastic stiffness. Thus, in this paper, by using a continuum modeling approach previously developed by the author based on both the principle of strain energy equivalence and the equivalent elliptical micro-crack representation of a local damage, the effective elastic compliance and effective engineering constants are derived in closed forms for both damaged two- and three-dimensional isotropic solids. They are derived in terms of the undamaged (virgin) elastic properties and a scalar damage variable.

Effective elastic properties of damaged isotropic solids

In continuum damage mechanics, damaged solids have been represented by the effective elastic stiffness into which local damage is smoothly smeared. Similarly, damaged solids may be represented in terms of effective elastic compliances. By virtue of the effective elastic compliance representation, it may become easier to derive the effective engineering constants of damaged solids from the effective elastic compliances, all in closed form. Thus, in this paper, by using a continuum modeling approach based on both the principle of strain energy equivalence and the equivalent elliptical micro-crack representation of local damage, the effective elastic compliance and effective engineering constants are derived in terms of the undamaged (virgin) elastic properties and a scalar damage variable for both damaged two- and three-dimensional isotropic solids.

An alternating method based on the VNA solution for analysis of damaged solid containing arbitrarily distributed elliptical microcracks

This paper presents the development of an alternating method for the interaction analysis of arbitrary distributed numerous elliptical microcracks. The complete analytical solutions (VNA solutions) for a single elliptical crack in an infinite solid, subject to arbitrary crack-face tractions, are implemented in the present alternating method, together with the coordinate transformations for stress tensors. First, the present method is verified by solving the problems of two interacting cracks for which accurate numerical solutions have been obtained previously. Next, the present method demonstrates obtaining efficient and accurate solutions for the problems of many interacting elliptical cracks, which cannot be solved in a practical sense by the ordinary numerical methods such as the finite element method. Furthermore, damaged solids containing periodically distributed elliptical microcracks are analyzed by the present alternating method. The effective elastic moduli are evaluated for varying microcrack density. Detailed structures of the interactions in the damaged solids are visualized and clarified.

信頼性工学 分布微小だ円き裂損傷材料の微視的および巨視的特性評価法

信頼性工学 分布微小だ円き裂損傷材料の微視的および巨視的特性評価法

Anisotropic damage mechanics based on strain energy equivalence and equivalent elliptical microcracks

A theory of damage mechanics is introduced based on a principle of strain energy equivalence. This principle is used to develop the effective continuum elastic properties of a damaged solid in terms of the undamaged elastic properties and a scalar damage field. The damage variable is defined as the volume fraction of a damage zone associated with equivalent elliptical microcracks. This definition provides a means by which a damaged isotropic material can exhibit anisotropic (orthotropic) properties, and entails determining effective crack orientation and geometry factors from the local deformation. Strain energy dissipation associated with crack growth (not nucleation) is used to develop a consistent damage evolution equation. This evolution equation is related to the standard power law model of crack growth commonly used in fracture mechanics, and to the equivalent stress measure commonly used in mechanics of plastic deformation. The combination of representing local damage as an effective elliptical crack volume fraction, a consistent damage evolution equation, and the determination of effective elastic properties using a strain energy equivalence principle yields a simple, yet powerful, approach to predicting failure of mechanical components.