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.

Moment Tensor Analysis of the Acoustic Emission Source in the Rock Damage Process

To further investigate the mechanism of acoustic emission (AE) in the rock fracture experiment, moment tensor analysis was carried out. The AE sources characterized by crack sizes, orientations and fracture modes, are represented by a time-dependent momen

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*.

Fractography and Crack Initiation of Very-High-Cycle Fatigue for a High Carbon Low Alloy Steel

Very-High-Cycle Fatigue (VHCF) is the phenomenon of fatigue damage and failure of metallic materials or structures subjected to 108 cycles of fatigue loading and beyond. This paper attempts to investigate the VHCF behavior and mechanism of a high strength low alloy steel (main composition: C-1% and Cr-1.5%; quenched at 1108K and tempered at 453K). The fractography of fatigue failure was observed by optical microscopy and scanning electron microscopy. The observations reveal that, for the number of cycles to fatigue failure between 106 and 4108 cycles, fatigue cracks almost initiated in the interior of specimen and originated at non-metallic inclusions. An “optical dark area” (ODA) around initiation site is observed when fatigue initiation from interior. ODA size increases with the decrease of fatigue stress, and becomes more roundness. Fracture mechanics analysis gives the stress intensity factor of ODA, which is nearly equivalent to the corresponding fatigue threshold of the test material. The results indicate that the fatigue life of specimens with crack origin at the interior of specimen is longer than that with crack origin at specimen surface. The experimental results and the fatigue mechanism were further analyzed in terms of fracture mechanics and fracture physics, suggesting that the primary propagation of fatigue crack within the fish-eye local region is the main characteristics of VHCF.

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.

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.

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.

Residual properties of an injection-molded poly(phenylene ether ketone) carbon composite during flexural fatigue

The present work investigates the effects of cyclic fatigue loading on the residual properties of an injection-molded composite, carbon-fiber-reinforced poly(phenylene ether ketone) (CF/PEK-C), and damage development in this material under fatigue lending. Test specimens, which had been conditioned to various preselected fatigue damage stages, were measured for their residual properties. The results indicated that cyclic fatigue loading alters the constitutive behavior of the injection-molded composite, especially in the non-linear portion of the stress/strain curve. The residual strength decreases with increase in the number of fatigue cycles as a consequence of the accumulation of fatigue damage, which is dominated by the growth of microcracks. While the residual modulus increases slightly with cyclic fatigue loading, this is probably due to the oriented hardening resulting from creep deformation which is induced during cyclic loading. (C) 1997 Elsevier Science Limited.

Corrosion fatigue of welded joints of steel for marine platform

Experiments on the corrosion fatigue behaviour of welded joints of the steel for marine platform in air and seawater, and of the joints in seawater with cathodic protection, yielded data for linear regression to obtain fatigue life curves (Delta S-N-f). The laws of corrosion fatigue in welded joints of test steel are discussed with reference to those of A(587) and A(131) steel. In these experiments, the fatigue damage occurring at all welded joints around the weld interface resulted in the cracks and fractures. The fatigue life of the specimens in seawater with cathodic protection is longer than that in seawater Without protection.

Mechanical fatigue and spectrum analysis of small-satellite

Mechanical fatigue due to environmental loads and spectrum analysis due to launch loads of the primary structure of a low cost, low-earth orbit small satellite intended for earth observation missions are presented. The payload of the satellite under consideration is a precise optical unit to image the earth’s surface having a mass of 45 kg. 3-D Finite Element Model for the satellite structure is generated by applying substructure method. Modal analysis is required to determine natural frequencies of the satellite and define its mode shape. Then, ranking of mode shapes according to specific constraint is performed. Harmonic analysis at resonance frequencies with the highest ranking is done and cumulative fatigue damage analysis is performed. Spectrum analysis is performed for Small Sat structure to verify the satellite structure reliability under all dynamic random vibration loads applied during transportation and launch cases.

Thermal fatigue analysis of solar panel structure for micro-satellite applications

Thermal fatigue analysis based on 2D finite difference and 3D finite element methods is carried out to study the performance of solar panel structure during micro-satellite life time. Solar panel primary structure consists of honeycomb structure and composite laminates. The 2D finite difference (I-DEAS) model yields predictions of the temperature profile during one orbit. Then, 3D finite element analysis (ANSYS) is applied to predict thermal fatigue damage of solar panel structure. Meshing the whole structure with 2D multi-layer shell elements with sandwich option is not efficient, as it misses thermal response of the honeycomb structure. So we applied a mixed approach between 3D solid and 2D shell elements to model the solar panel structure without the sandwich option.

A micromechanics approach for damage modeling of polymer matrix composites

A new model for damage evolution in polymer matrix composites is presented. The model is based on a combination of two constituent-level models and an interphase model. This approach reduces the number of empirical parameters since the two constituent- level models are formulated for isotropic materials, namely fiber and matrix. Decomposition of the state variables down to the micro-scale is accomplished by micromechanics. Phenomenological damage evolution models are then postulated for each constituent. Determination of material parameters is made from available experimental data. The required experimental data can be obtained with standard tests. Comparison between model predictions and additional experimental data is presented.