A new micromechanical formulation of martensite kinetics driven by temperature and/or stress

Summary Martensitic transformation behavior of alloys is studied under the arbitrary action of a thermal and/or a triaxial mechanical load-stress state by solving a transformation kinetic equation presented recently by the same authors. Numerical and analytical solutions reveal that the transformation behavior is almost path-independent. Lines of constant volume fraction of martensite are nearly parallel in the stress-temperature plane. Some new analytical formulae for martensitic transformation kinetics are presented.

---

Eine neue mikromechanische Formulierung der Martensit-Kinetik unter Temperatur- und/order Spannungsbelastung

Übersicht Es wird das Verhalten der martensitischen Umwandlung von Legierungen unter beliebiger thermischer und/oder dreiachsiger mechanischer Spannungsbelastung untersucht, indem eine neue Gleichung der Umwandlungskinetik gelöst wird. Diese Gleichung wurde vor kurzem von denselben Autoren vorgestellt. Die numerischen und die analytischen Lösungen zeigen, daß das Transformationsverhalten nahezu pfadunabhängig ist. Die Linien gleicher Volumsfraktion von Martensit sind nahezu parallel im Spannungs-Temperatur-Diagramm. Es werden auch einige neue analytische Formeln für die Umwandlungskinetik von Martensit präsentiert.

     

Single-camera Doppler global velocimetry based on frequency modulation techniques

The main advantage of the described Doppler global velocimeter (DGV) systems based on frequency modulation (FM) or frequency shift keying (FSK) is that no reference detector is required. The frequency variation of the laser light during one modulation period additionally allows an on-line calibration of the complete DGV system. Thus, the new method has the potential to reduce the uncertainty of conventional DGV velocity measurements since time resolved velocity field measurements on a spinning disc have shown standard deviations down to 0.02 m/s. On investigating flow fields, velocity components notably less than 0.5 m/s were resolved.     

Inhomogeneity effects on the crack driving force in elastic and elastic-plastic materials

This article evaluates the effect of material inhomogeneities on the crack-tip driving force in general inhomogeneous bodies and reports results for bimaterial composites. The theoretical model, based on Eshelby material forces, makes no assumptions about the distribution of the inhomogeneities or the constitutive properties of the materials. Inhomogeneities are modeled by making the stored energy have an explicit dependence on the reference coordinates. Then the material inhomogeneity effect on the crack-tip driving force is quantified by the term C_inh, which is the integral of the gradient of the stored energy in the direction of crack growth. The model is demonstrated by two model problems: (i) bimaterial elastic composite using asymptotic solutions and (ii) graded elastic and elastic-plastic compact tension specimen using numerical methods for stress analysis.     

A minimal model for studying properties of the mode-coupling type instability in friction induced oscillations

A minimal two degree of freedom model is used to clarify from an intuitive perspective the physical mechanisms underlying the mode-coupling instability of self-excited friction induced oscillations. It is shown that simultaneous out-of-phase oscillations of friction force and displacement tangential to the friction force may lead to energy transfer from the frictional system to vibrational energy. Also it is shown that the friction force acts like a cross-coupling force linking motion normal to the contact surface to motion parallel to it and that a necessary condition for the onset of instability is that these friction-induced cross-coupling forces balance the corresponding structural cross-coupling forces of the system. Finally the origin and the role of phase shifts between oscillations normal and parallel to the contact surface is clarified with respect to the mode-coupling instability. It may be expected that the intuitive picture gained will be of considerable help for practical design purposes.     

Review of brittle fracture criteria in case of static and cyclic mixed mode loading

The paper gives in the first part in pressed form a survey of brittle fracture criteria using a reference intensity factor in case of static mixed mode loading. Criteria (expressed in terms of different quantities such as stress, deformation and strain energy) usually refer to a parameter that is characteristic of the material response at fracture. Criteria include information on two basic hypotheses (crack propagation direction and unstable crack growth). In the second part a generalized method is suggested for application of cyclic reference intensity factor in case of cyclic mixed mode loading. Three basic hypotheses describe crack growth direction, stable crack growth steps and unstable crack growth.     

Application of material forces to fracture of inhomogeneous materials: illustrative examples

The material forces concept has become an elegant tool in continuum mechanics for the calculation of the thermodynamic driving force of a defect. Based on this concept, we have recently shown that inhomogeneities essentially shield or anti-shield crack tips from applied far-field stresses. The goal of this paper is to illustrate this by considering the model example of a crack in a CT-type specimen that contains a bimaterial interface. The crack driving force is calculated as the sum of the far-field driving force and the crack-tip shielding or anti-shielding. Several cases of inhomogeneity in either thermal or elastic properties are considered. Rather simple hand calculations are provided in addition to numerical results to illustrate the advantages of using the material forces concept.     

Global Existence of Renormalized Solutions to Entropy-Dissipating Reaction–Diffusion Systems

Archive for Rational Mechanics and Analysis - In the present work we introduce the notion of a renormalized solution for reaction–diffusion systems with entropy-dissipating reactions. We...