Mengfen Xia

Damage evolution, localization and failure of solids subjected to impact loading

In order to reveal the underlying mesoscopic mechanism governing the experimentally observed failure in solids subjected to impact loading, this paper presents a model of statistical microdamage evolution to macroscopic failure, in particular to spallation. Based on statistical microdamage mechanics and experimental measurement of nucleation and growth of microcracks in an Al alloy subjected to plate impact loading, the evolution law of damage and the dynamical function of damage are obtained. Then, a lower bound to damage localization can be derived. It is found that the damage evolution beyond the threshold of damage localization is extremely fast. So, damage localization can serve as a precursor to failure. This is supported by experimental observations. On the other hand, the prediction of failure becomes more accurate, when the dynamic function of damage is fitted with longer experimental observations. We also looked at the failure in creep with the same idea. Still, damage localization is a nice precursor to failure in creep rupture.

Evolution induced catastrophe

Abstract Fracture due to coalescence of microcracks seems to be catalogued in a new model of evolution induced catastrophe (EIC). The key underlying mechanism of the EIC is its automatically enlarging interaction of microcraks. This leads to an explosively evolving catastrophe. Most importantly, the EIC presents a fractal dimension spectrum which appears to be dependent on the interaction.

Damage Field Equation and Criterion for Damage Localization

For heterogeneous materials with distributed microcracks or microvoids, damage evolution should be described in terms of a system of damage field and continuum mechanics equations. It was found that the dynamic function of damage f=f (D, σ), i.e. the intrinsic damage evolution rate and the macroscopic formulation of the nucleation, growth and coalescence of microdamages, plays a key role in the evolution. The population of microdamages has a tendency to form localized damage, namely a precursor to failure. The increase of the relative gradient of damage signifies the occurrence of damage localization. Under quasistatic small deformation in one dimensional strain state, this leads to the following criteria f D >f/D+θ and f D >f/D in Eulerian and Lagrangian co-ordinates respectively, where θ is dilatation rate. Whereas under the same assumptions the criterion for maximum stress is f;=θ Clearly, damage localization is a distinct feature of solids. It is relevant to the attainment of maximum stress via the dynamic function of damage f.

Evolution of Localized Damage Zone in Heterogeneous Media

Evolution of localized damage zone is a key to catastrophic rupture in heterogeneous materials. In the present article, the evolutions of strain fields of rock specimens are investigated experimentally. The observed evolution of fluctuations and autocorrelations of strain fields under uniaxial compression demonstrates that the localization of deformation always appears ahead of catastrophic rupture. In particular, the localization evolves pronouncedly with increasing deformation in the rock experiments. By means of the definition of the zone with high strain rate and likely damage localization, it is found that the size of the localized zone decreases from the sample size at peak load to an eventual value. Actually, the deformation field beyond peak load is bound to suffer bifurcation, namely an elastic unloading part and a continuing but localized damage part will co-exist in series in a specimen. To describe this continuous bifurcation and localization process observed in experiments, a model on continuum mechanics is developed. The model can explain why the decreasing width of localized zone can lead stable deformation to unstable, but it still has not provided the complete equations governing the evolution of the localized zone.

Evolution-induced Catastrophe and its Predictability

Both earthquake prediction and failure prediction of disordered brittle media are difficult and complicated problems and they might have something in common. In order to search for clues for earthquake prediction, the common features of failure in a simple nonlinear dynamical model resembling disordered brittle media are examined. It is found that the failure manifests evolution-induced catastrophe (EIC), i.e., the abrupt transition from globally stable (GS) accumulation of damage to catastrophic failure. A distinct feature is the significant uncertainty of catastrophe, called sample-specificity. Consequently, it is impossible to make a deterministic prediction macroscopically. This is similar to the question of predictability of earthquakes. However, our model shows that strong stress fluctuations may be an immediate precursor of catastrophic failure statistically. This might provide clues for earthquake forecasting.

Damage Localization as a Possible Precursor of Earthquake Rupture

Based on the concepts of statistical mesoscopic damage mechanics, the rupture of a heterogeneous medium is investigated in terms of numerical simulations of a network model, subjected to simple shear loading. The heterogeneities are simulated by varying the sizes and fracture strains of the elements of the network. Progressive damage is governed by a damage field equation and a dynamic function of damage (DFD). From the damage field equation, a criterion for damage localization can be derived, and the DFD can be extracted from the simulations of the network. Importantly, the DFD intrinsically governs the damage localization. Both stress-free and periodic boundary conditions for the network are examined. It is found that damage localization may be the underlying mechanism of eventual rupture and thus could be used as a possible precursor of earthquake rupture.

Statistical microdamage mechanics and damage field evolution

Discussed are the underlying background of statistical microdamage mechanics, the fundamental partial differential equation of evolution of microdamage number density, two basic solutions, and the saturation of microdamage number density evolution. Knowledge of microdamage number density evolution is applied to engineering practice by using the field equations of microdamage number density and continuum damage. The addition of continuum equations renders a complete system of field equations of deformation and damage. However, they are open-ended in character at the continuum level although the dynamic damage function is completed from the meso- to the macro-scale level. Once decoupling of the function is made, the system of equations can be connected in an approximate manner. This provides a reasonable approximation to the continuum field of deformation and damage. The open literature prediction based on damage evolution relies on assuming arbitrary critical damage states. In this work, use is made of the criterion for damage localization. Several applications of statistical microdamage mechanics are made. This includes damage evolution in a heterogeneous medium and failure forecast under impact. The results show that statistical microdamage mechanics and the derived closed approximate continuum formulations are physically sound and practically effective.

Threshold diversity and trans-scales sensitivity in a finite nonlinear evolution model of materials failure

We present a slice-sampling method and study the ensemble evolution of a large finite nonlinear system in order to model materials failure. There is a transitional region of failure probability. Its size effect is expressed by a slowly decaying scaling law. In a meso-macroscopic range (similar to 10(5)) in realistic failure, the diversity cannot be ignored. Sensitivity to mesoscopic details governs the phenomena

Adaptive Mesh Refinement FEM for Damage Evolution of Heterogeneous Brittle Media

Damage evolution of heterogeneous brittle media involves a wide range of length scales. The coupling between these length scales is the underlying mechanism of damage evolution and rupture. However, few of previous numerical algorithms consider the effects of the trans-scale coupling effectively. In this paper, an adaptive mesh refinement finite element method (FEM) algorithm is developed to simulate this trans-scale coupling. The adaptive serendipity element is implemented in this algorithm, and several special discontinuous base functions are created to avoid the incompatible displacement between the elements. Both the benchmark and a typical numerical example under quasi-static loading are given to justify the effectiveness of this model. The numerical results reproduce a series of characteristics of damage and rupture in heterogeneous brittle media.

Evolution Induced Catastrophe in a Nonlinear Dynamical Model of Material Failure

In order to study the failure of disordered materials, theensemble evolution of a nonlinear chain model was examined by using astochastic slice sampling method. The following results were obtained.(1) Sample-specific behavior, i.e. evolutions are different from sampleto sample in some cases under the same macroscopic conditions, isobserved for various load-sharing rules except in the globally meanfield theory. The evolution according to the cluster load-sharing rule,which reflects the interaction between broken clusters, cannot bepredicted by a simple criterion from the initial damage pattern and eventhen is most complicated. (2) A binary failure probability, itstransitional region, where globally stable (GS) modes andevolution-induced catastrophic (EIC) modes coexist, and thecorresponding scaling laws are fundamental to the failure. There is asensitive zone in the vicinity of the boundary between the GS and EICregions in phase space, where a slight stochastic increment in damagecan trigger a radical transition from GS to EIC. (3) The distribution ofstrength is obtained from the binary failure probability. This, likesample-specificity, originates from a trans-scale sensitivity linkingmeso-scopic and macroscopic phenomena. (4) Strong fluctuations in stressdistribution different from that of GS modes may be assumed as aprecursor of evolution-induced catastrophe (EIC).