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.

Methods of Obtaining Instantaneous Modulus of Viscoelastic Solids Using Displacement-Controlled Instrumented Indentation with Axisymmetric Indenters of Arbitrary Smooth Profiles

We derive a relationship between the initial unloading slope, contact depth, and the instantaneous relaxation modulus for displacement-controlled indentation in linear viscoelastic solids by a rigid indenter with an arbitrary axisymmetric smooth profile. While the same expression is well known for indentation in elastic and in elastic–plastic solids, we show that it is also true for indentation in linear viscoelastic solids, provided that the unloading rate is sufficiently fast. When the unloading rate is slow, a “hold” period between loading and unloading can be used to provide a correction term for the initial unloading slope equation. Finite element calculations are used to illustrate the methods of fast unloading and “hold-at-the-maximum-indenter-displacement” for determining the instantaneous modulus using spherical indenters.

Mechanical Properties And Constitutive Relationships Of 30Crmnsia Steel Heated At High Rate

In this paper, the mechanical behavior of 30CrMnSiA steel after heating at a high rate are investigated experimentally and theoretically, including a detailed discussion of the effects of strain rate and temperature. Two constitutive models are presented to describe the mechanical response of this material after heating at a high rate, and verified by experimental results. (C) 2007 Elsevier B.V. All rights reserved.

The Pressure Transient Analysis Of Deformation Of Fractal Medium

The assumption of constant rock properties in pressure-transient analysis of stress-sensitive reservoirs can cause significant errors in the estimation of temporal and spatial variation of pressure. In this article, the pressure transient response of the fractal medium in stress-sensitive reservoirs was studied by using the self-similarity solution method and the regular perturbation method. The dependence of permeability on pore pressure makes the flow equation strongly nonlinear. The nonlinearities associated with the governing equation become weaker by using the logarithm transformation. The perturbation solutions for a constant pressure production and a constant rate production of a linear-source well were obtained by using the self-similarity solution method and the regular perturbation method in an infinitely large system, and inquire into the changing rule of pressure when the fractal and deformation parameters change. The plots of typical pressure curves were given in a few cases, and the results can be applied to well test analysis.

Atomistic Origin Of Rate-Dependent Serrated Plastic Flow In Metallic Glasses

Nanoindentation simulations on a binary metallic glass were performed under various strain rates by using molecular dynamics. The rate-dependent serrated plastic flow was clearly observed, and the spatiotemporal behavior of its underlying irreversible atomic rearrangement was probed. Our findings clearly validate that the serration is a temporally inhomogeneous characteristic of such rearrangements and not directly dependent on the resultant shear-banding spatiality. The unique spatiotemporal distribution of shear banding during nanoindentation is highlighted in terms of the potential energy landscape (PEL) theory.

Molecular Dynamics Study Of The Mechanical Behavior Of Nickel Nanowire: Strain Rate Effects

We present the analysis of uniaxial deformation of nickel nanowires using molecular dynamics simulations, and address the strain rate effects on mechanical responses and deformation behavior. The applied strain rate is ranging from 1 x 10(8) s(-1) to 1.4 x 10(11) s(-1). The results show that two critical strain rates, i.e., 5 x 10(9) s(-1) and 8 x 10(10) s(-1), are observed to play a pivotal role in switching between plastic deformation modes. At strain rate below 5 x 10(9) s(-1), Ni nanowire maintains its crystalline structure with neck occurring at the end of loading, and the plastic deformation is characterized by {111} slippages associated with Shockley partial dislocations and rearrangements of atoms close to necking region. At strain rate above 8x10(10) s(-1), Ni nanowire transforms from a fcc crystal into a completely amorphous state once beyond the yield point, and hereafter it deforms uniformly without obvious necking until the end of simulation. For strain rate between 5 x 10(9) s(-1) and 8 x 10(10) s(-1), only part of the nanowire exhibits amorphous state after yielding while the other part remains crystalline state. Both the {111} slippages in ordered region and homogenous deformation in amorphous region contribute to the plastic deformation. (C) 2007 Published by Elsevier B.V.

A Modified Free Volume Model For Characterizing Of Rate Effect In Bulk Metallic Glasses

We investigate the plastic deformation and constitutive behaviour of bulk metallic glasses (BMGs). A dimensionless Deborah number De(ID) = t(r)/t(i) is proposed to characterize the rate effect in BMGs, where t(r) is the structural relaxing characteristic time of BMGs under shear load, t(i) is the macroscopic imposed characteristic time of applied stress or the characteristic time of macroscopic deformation. The results demonstrate that the modified free volume model can characterize the strain rate effect in BMGs effectively.

A theoretical analysis on stochastic behaviour of short cracks and fatigue damage of metals

In this paper, the closed form of solution to the stochastic differential equation for a fatigue crack evolution system is derived. and the relationship between metal fatigue damage and crack stochastic behaviour is investigated. It is found that the damage extent of metals is independent of crack stochastic behaviour ii the stochastic deviation of the crack growth rate is directly proportional to its mean value. The evolution of stochastic deviation of metal fatigue damage in the stage close to the transition point between short and long crack regimes is also discussed.

Gain saturation effects of a flowing chemical oxygen-iodine laser

A new oxygen-iodine medium gain model is developed to include pumping and deactivation of the upper laser levels of the iodine atoms, hyperfine and translation relaxation, as well as the flowing effect. The rate equations for gain of a supersonic flowing cw oxygen-iodine laser (COIL) are described when the medium is stimulated by a single-mode field. The general solution of the self-consistency integral equation is obtained. The result shows that the saturation behaviour in low pressure of the COIL differs from both the inhomogeneous and homogeneous broadening, and exhibits an 'anomalous' saturation phenomenon.

Study on improving the turbidity measurement of the absolute coagulation rate constant

The existing theories dealing with the evaluation of the absolute coagulation rate constant by turbidity measurement were experimentally tested for different particle-sized (radius = a) suspensions at incident wavelengths (lambda) ranging from near-infrared to ultraviolet light. When the size parameter alpha = 2 pi a/lambda > 3, the rate constant data from previous theories for fixed-sized particles show significant inconsistencies at different light wavelengths. We attribute this problem to the imperfection of these theories in describing the light scattering from doublets through their evaluation of the extinction cross section. The evaluations of the rate constants by all previous theories become untenable as the size parameter increases and therefore hampers the applicable range of the turbidity measurement. By using the T-matrix method, we present a robust solution for evaluating the extinction cross section of doublets formed in the aggregation. Our experiments show that this new approach is effective in extending the applicability range of the turbidity methodology and increasing measurement accuracy.

Toward an understanding of the turbidity measurement of fleterocoagulation rate constants of dispersions containing particles of different sizes

Our previous studies have shown that the determination of coagulation rate constants by turbidity measurement becomes impossible for a certain operating wavelength (that is, its blind point) because at this wavelength the change in the turbidity of a dispersion completely loses its response to the coagulation process. Therefore, performing the turbidity measurement in the wavelength range near the blind point should be avoided. In this article, we demonstrate that the turbidity measurement of the rate constant for coagulation of a binary dispersion containing particles of two different sizes (heterocoagulation) presents special difficulties because the blind point shifts with not only particle size but also with the component fraction. Some important aspects of the turbidity measurement for the heterocoagulation rate constant are discussed and experimentally tested. It is emphasized that the T-matrix method can be used to correctly evaluate extinction cross sections of doublets formed during the heterocoagulation process, which is the key data determining the rate constant from the turbidity measurement, and choosing the appropriate operating wavelength and component fraction are important to achieving a more accurate rate constant. Finally, a simple scheme in experimentally determining the sensitivity of the turbidity changes with coagulation over a wavelength range is proposed.

Partial-mediated slips in nanocrystalline Ni at high strain rate

Previous experiments on nanocrystalline Ni were conducted under quasistatic strain rates (similar to 3x10(-3)/s), which are much lower than that used in typical molecular dynamics simulations (>3x10(7)/s), thus making direct comparison of modeling and experiments very difficult. In this study, the split Hopkinson bar tests revealed that nanocrystalline Ni prefers twinning to extended partials, especially under higher strain rates (10(3)/s). These observations contradict some reported molecular dynamics simulation results, where only extended partials, but no twins, were observed. The accuracy of the generalized planar fault energies is only partially responsible, but cannot fully account for such a difference. (C) 2007 American Institute of Physics.

Thermal stress wave and spallation induced by an electron beam

Thermal stress wave and spallation in aluminium alloy exposed to a high fluency and low energy electron beams are studied theoretically. A simple model for the study of energy deposition of electrons in materials is presented on the basis of some empirical formulae. Under the stress wave induced by energy deposition, microcracks and/or microvoids may appear in target materials, and in this case, the inelastic volume deformation should not vanish. The viscoplastic model proposed by Bodner and Partom with corresponding Gurson's yield function requires modification for this situation. The new constitutive model contains a scalar field variable description of the material damage which is taken as the void volume fraction of the polycrystalline material. Incorporation of the damage parameter permits description of rate-dependent, compressible, inelastic deformation and ductile fracture. The melting phenomenon has been observed in the experiment, therefore one needs to take into account the melting process in the intermediate energy deposition range. A three-phase equation of state used in the paper provides a more detailed and thermodynamical description of metals, particularly, in the melting region. The computational results based on the suggested model are compared with the experimental test for aluminium alloy, which is subjected to a pulsed electron beam with high fluency and low energy. (C) 1997 Elsevier Science Ltd.