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.

On the mechanism of void growth and the effect of straining mode in ductile materials

Finite element analysis is employed to investigate void growth embedded in elastic-plastic matrix material. Axisymmetric and plane stress conditions are considered. The simulation of void growth in a unit cell model is carried out over a wide range of triaxial tensile stressing or large plastic straining for various strain hardening materials to study the mechanism of void growth in ductile materials. Triaxial tension and large plastic strain encircling around the void are found to be of most importance for driving void growth. The straining mode of incremental loading which favors the necessary strain concentration around void for its growth can be characterized by the vanishing condition of a parameter called "the third invariant of generalized strain rate". Under this condition, it accentuates the internal strain concentration and the strain energy stored/dissipated within the material layer surrounding the void. Experimental results are cited to justify the effect of this loading parameter. (C) 2000 Elsevier Science Ltd. All rights reserved.

Influence of inertial and thermal effects on the dynamic growth of voids in porous ductile materials

The influence of inertial, thermal and rate - sensitive effects on the void growth at high strain rate in a thermal - viscoplastic solid is investigated by means of a theoretical model presented in the present paper. Numerical analysis of the model suggests that inertial, thermal and rate - sensitive effects are three major factors which greatly influence the behavior of void growth in the high strain rate case. Comparison of the mathematical model proposed in the present work and Johnson's model shows that if the temperature - dependence is considered, material viscosity eta can take the experimentally measured values.

Crack tip behavior and crack-propagation in ductile materials

Dilatational plastic equations, which can include the effects of ductile damage, are derived based on the equivalency in expressions for dissipated plastic work. Void damage developed internally at the large-strain stage is represented by an effective continuum being strain-softened and plastically dilated. Accumulation of this local damage leads to progressive failure in materials. With regard to this microstructural background, the constitutive parameters included for characterizing material behaviour have the sense of internal variables. They are not able to be determined explicitly by macroscopic testing but rather through computer simulation of experimental curves and data. Application of this constitutive model to mode-I cracking examples demonstrates that a huge strain concentration accompanied by a substantial drop of stress does occur near the crack tip. Eventually, crack propagation is simulated by using finite elements in computations. Two numerical examples show good accordance with experimental data. The whole procedure of study serves as a justification of the constitutive formulation proposed in the text.

On dilatational plastic constitutive equation of ductile materials and plastic loading paths at bifurcation

The dilatational plastic constitutive equation presented in this paper is proved to be in a form of generality. Based on this equation, the constitutive behaviour of materials at the moment of bifurcation is demonstrated to follow a loading path with the response as "soft" as possible.

Dynamic failure in ductile porous materials

In this paper, a mathematical model of dynamic fracture in porous ductile materials under intense dynamic general loading is developed. The mathematical model includes the influence of inertial effects and material rate sensitivity, as well as the contribution of surface energy of a void and material work-hardening. In addition, the condition of the void compaction is considered as well. The threshold stresses for the void growth and compaction are obtained. A simple criterion for ductile fracture which is associated with material distention and plastic deformation is adopted. As an application of the theoretical model, the processes of two-dimensional spallation in LY12 aluminum alloy are successfully simulated by means of two-dimensional finite-difference Lagrangian code.

Toughness & cutting: A new way of determining ductile fracture toughness and strength

A review is given of the mechanics of cutting, ranging from the slicing of thin floppy offcuts (where there is negligible elasticity and no permanent deformation of the offcut) to the machining of ductile metals (where there is severe permanent distortion of the offcut/chip). Materials scientists employ the former conditions to determine the fracture toughness of ‘soft’ solids such as biological materials and foodstuffs. In contrast, traditional analyses of metalcutting are based on plasticity and friction only, and do not incorporate toughness. The machining theories are inadequate in a number of ways but a recent paper has shown that when ductile work of fracture is included many, if not all, of the shortcomings are removed. Support for the new analysis is given by examination of FEM simulations of metalcutting which reveal that a ‘separation criterion’ has to be employed at the tool tip. Some consideration shows that the separation criteria are versions of void-initiation-growth-and-coalescence models employed in ductile fracture mechanics. The new analysis shows that cutting forces for ductile materials depend upon the fracture toughness as well as plasticity and friction, and reveals a simple way of determining both toughness and flow stress from cutting experiments. Examples are given for a wide range of materials including metals, polymers and wood, and comparison is made with the same properties independently determined using conventional testpieces. Because cutting can be steady state, a new way is presented for simultaneously measuring toughness and flow stress at controlled speeds and strain rates.

Yield criterion of porous materials subjected to complex stress states

Finite-element simulations are used to obtain many thousands of yield points for porous materials with arbitrary void-volume fractions with spherical voids arranged in simple cubic, body-centred cubic and face-centred cubic three-dimensional arrays. Multi-axial stress states are explored. We show that the data may be fitted by a yield function which is similar to the Gurson-Tvergaard-Needleman (GTN) form, but which also depends on the determinant of the stress tensor, and all additional parameters may be expressed in terms of standard GTN-like parameters. The dependence of these parameters on the void-volume fraction is found. (c) 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Yield functions for porous materials with cubic symmetry using different definitions of yield

Plastic yield criteria for porous ductile materials are explored numerically using the finite-element technique. The cases of spherical voids arranged in simple cubic, body-centred cubic and face-centred cubic arrays are investigated with void volume fractions ranging from 2 % through to the percolation limit (over 90 %). Arbitrary triaxial macroscopic stress states and two definitions of yield are explored. The numerical data demonstrates that the yield criteria depend linearly on the determinant of the macroscopic stress tensor for the case of simple-cubic and body-centred cubic arrays - in contrast to the famous Gurson-Tvergaard-Needleman (GTN) formula - while there is no such dependence for face-centred cubic arrays within the accuracy of the finite-element discretisation. The data are well fit by a simple extension of the GTN formula which is valid for all void volume fractions, with yield-function convexity constraining the form of the extension in terms of parameters in the original formula. Simple cubic structures are more resistant to shear, while body-centred and face-centred structures are more resistant to hydrostatic pressure. The two yield surfaces corresponding to the two definitions of yield are not related by a simple scaling.

Analysis of acoustic emission data for accurate damage assessment for structural health monitoring applications

Structural health monitoring (SHM) refers to the procedure used to assess the condition of structures so that their performance can be monitored and any damage can be detected early. Early detection of damage and appropriate retrofitting will aid in preventing failure of the structure and save money spent on maintenance or replacement and ensure the structure operates safely and efficiently during its whole intended life. Though visual inspection and other techniques such as vibration based ones are available for SHM of structures such as bridges, the use of acoustic emission (AE) technique is an attractive option and is increasing in use. AE waves are high frequency stress waves generated by rapid release of energy from localised sources within a material, such as crack initiation and growth. AE technique involves recording these waves by means of sensors attached on the surface and then analysing the signals to extract information about the nature of the source. High sensitivity to crack growth, ability to locate source, passive nature (no need to supply energy from outside, but energy from damage source itself is utilised) and possibility to perform real time monitoring (detecting crack as it occurs or grows) are some of the attractive features of AE technique. In spite of these advantages, challenges still exist in using AE technique for monitoring applications, especially in the area of analysis of recorded AE data, as large volumes of data are usually generated during monitoring. The need for effective data analysis can be linked with three main aims of monitoring: (a) accurately locating the source of damage; (b) identifying and discriminating signals from different sources of acoustic emission and (c) quantifying the level of damage of AE source for severity assessment. In AE technique, the location of the emission source is usually calculated using the times of arrival and velocities of the AE signals recorded by a number of sensors. But complications arise as AE waves can travel in a structure in a number of different modes that have different velocities and frequencies. Hence, to accurately locate a source it is necessary to identify the modes recorded by the sensors. This study has proposed and tested the use of time-frequency analysis tools such as short time Fourier transform to identify the modes and the use of the velocities of these modes to achieve very accurate results. Further, this study has explored the possibility of reducing the number of sensors needed for data capture by using the velocities of modes captured by a single sensor for source localization. A major problem in practical use of AE technique is the presence of sources of AE other than crack related, such as rubbing and impacts between different components of a structure. These spurious AE signals often mask the signals from the crack activity; hence discrimination of signals to identify the sources is very important. This work developed a model that uses different signal processing tools such as cross-correlation, magnitude squared coherence and energy distribution in different frequency bands as well as modal analysis (comparing amplitudes of identified modes) for accurately differentiating signals from different simulated AE sources. Quantification tools to assess the severity of the damage sources are highly desirable in practical applications. Though different damage quantification methods have been proposed in AE technique, not all have achieved universal approval or have been approved as suitable for all situations. The b-value analysis, which involves the study of distribution of amplitudes of AE signals, and its modified form (known as improved b-value analysis), was investigated for suitability for damage quantification purposes in ductile materials such as steel. This was found to give encouraging results for analysis of data from laboratory, thereby extending the possibility of its use for real life structures. By addressing these primary issues, it is believed that this thesis has helped improve the effectiveness of AE technique for structural health monitoring of civil infrastructures such as bridges.

Damage mechanisms in stainless steel and chromium carbide coatings under controlled environment fretting conditions

Fretting is of a serious concern in many industrial components, specifically, in nuclear industry for the safe and reliable operation of various component and/or system. Under fretting condition small amplitude oscillations induce surface degradation in the form of surface cracks and/or surface wear. Comprehensive experimental studies have been carried out simulating different fretting regimes under ambient and vacuum (10(-9) MPa) conditions and, temperature up to 400 degrees C. Studies have been carried out with stainless steel spheres on stainless steel flats, and stainless steel spheres against chromium carbide, with 25% nickel chrome binder coatings. Mechanical responses are correlated with the damage observed. It has been observed that adhesion plays a vital role in material degradation process, and its effectiveness depends on mechanical variables such as normal load, interfacial tangential displacement, characteristics of the contacting bodies and most importantly on the environment conditions. Material degradation mechanism for ductile materials involved severe plastic deformation, which results in the initiation or nucleation of cracks. Ratcheting has been observed as the governing damage mode for crack nucleation under cyclic tangential loading condition. Further, propagation of the cracks has been observed under fatigue and their orientation has been observed to be governed by the contact conditions prevailing at the contact interface. Coated surfaces show damage in the form of brittle fracture and spalling of the coatings. Existence of stick slip has been observed under high normal load and low displacement amplitude. It has also been observed that adhesion at the contact interface and instantaneous cohesive strength of the contacting bodies dictates the occurrence of material transfer. The paper discusses the mechanics and mechanisms involved in fretting damage under controlled environment conditions. (C) 2015 Elsevier B.V. All rights reserved.

The Flow Theory of Mechanism-Based Strain Gradient Plasticity

The flow theory of mechanism-based strain gradient (MSG) plasticity is established in this paper following the same multiscale, hierarchical framework for the deformation theory of MSG plasticity in order to connect with the Taylor model in dislocation mechanics. We have used the flow theory of MSG plasticity to study micro-indentation hardness experiments. The difference between deformation and flow theories is vanishingly small, and both agree well with experimental hardness data. We have also used the flow theory of MSG plasticity to investigate stress fields around a stationary mode-I crack tip as well as around a steady state, quasi-statically growing crack tip. At a distance to crack tip much larger than dislocation spacings such that continuum plasticity still applies, the stress level around a stationary crack tip in MSG plasticity is significantly higher than that in classical plasticity. The same conclusion is also established for a steady state, quasi-statically growing crack tip, though only the flow theory can be used because of unloading during crack propagation. This significant stress increase due to strain gradient effect provides a means to explain the experimentally observed cleavage fracture in ductile materials [J. Mater. Res. 9 (1994) 1734, Scripta Metall. Mater. 31 (1994) 1037; Interface Sci. 3(1996) 169].

Numerical analyses for the material bifurcation in plane sheet under tension

The various patterns (shear banding, surface wrinkling and necking) of material bifurcation in plane sheet under tension are investigated in this paper by means of a numerical method. It is found that numerical analysis can provide better ground for searching for the lowest critical loads. The inhomogeneity caused by void damage and the nonuniformity in the stress distribution across sheet thickness are proved to have detrimental effects on the material bifurcation. Nevertheless, material stability can be promoted by any means of depressing void damage or alleviating stress, even locally across the thickness. Besides, the peculiar behaviour of material bifurcation under slight biaxiality state is demonstrated. Copyright (C) 1996 Elsevier Science Ltd

Selección de métodos de análisis de fatiga para ejes de transmisiones de máquinas.

[ES]Existe un elevado número de métodos para cálculos de fatiga en piezas sometidas a estados de tensiones multiaxiales. Cada método tiene un campo óptimo de aplicación: para materiales dúctiles, frágiles, estados con y sin tensiones medias, etc. En este Trabajo de Fin de Grado se trata de estudiar la precisión que proporcionan diferentes métodos de enfoque global (no de plano crítico) y comparar sus resultados a fin de decidir cuáles son los idóneos para los casos de carga más frecuentes en los ejes de transmisiones en automóviles.