Elena Sitnikova

Thermal Effect in Dynamic Yielding and Fracture of Metals and Alloys

The explanation of transition between ductile and brittle modes of fracture based on the “incubation time” concept is proposed. This approach allows us to establish relation between the influences of different loading parameters (strain-rate, temperature) on the mode of fracture. Proposed criteria give explanation to anomalous behavior of yield limit and possible high-temperature embrittlement.

EXPERIMENTAL BIFURCATIONS OF AN IMPACT OSCILLATOR WITH SMA CONSTRAINT

In this paper we study bifurcations of an impact oscillator with one sided SMA motion constraint. The excitation frequency is used as a bifurcation parameter and two different values of the excitation amplitude are considered. It is shown that as frequency varies, the system exhibits highly nonlinear behavior. A typical bifurcation diagram has a number of resonance regions separated by chaotic motions with additional windows of periodic responses. The evolution of chaotic attractors is recorded experimentally, and changes in the structure of the attractors are shown. A mathematical model is developed and the results of the simulations are compared with the experimental findings. It is shown that the model is capable of accurately predicting not only the resonance structure but also the shape of the periodic and chaotic attractors. Numerical investigations also reveal a number of coexisting attractors at some frequency values. In particular, three attractors are found numerically for A = 0.2 mm and f = 29.474 Hz and their basins of attraction are presented. For A = 0.2 mm and f = 33.463 Hz, four coexisting attractors are found. For both parameter sets, one of the numerically detected attractors was validated experimentally. The undertaken analysis has shown that the hysteretic behavior of the restraint affected the dynamic responses only at the resonances, when the displacements are sufficiently large to trigger phase transformations in the SMA restraint. In nonresonant frequency ranges the restoring force in the SMA constraint is elastic. These findings are consistent with the numerical analysis carried out in [Sitnikova et al., 2008] for a similar system, which showed that the hysteretic behavior of the SMA affects resonant responses and provides a substantial vibration reduction in those regions.

Dynamic Cracking Resistance of Structural Materials Predicted from Impact Fracture of an Aircraft Alloy

A new approach to studying the dynamic strength properties of structural materials is demonstrated with fracture of 2024-T3 aircraft aluminum alloy. The central idea of this approach is the incubation time to failure. In [1], experimental data for dynamic fracture of this alloy were analyzed in terms of the classical fracture criterion, which is based on the principle of maximum critical stress intensity factor [2]. In [1], the dependence of the stress intensity factor limiting value (the dynamic fracture toughness KId, which was assumed to be a functional characteristic of the material) on the loading rate was also measured. The same experimental data were analyzed in terms of an alternative structure-time approach [3]. In this approach, the dynamic fracture toughness KId is considered as an estimable characteristic of the problem, so that determination of limiting loads does not require a priori knowledge of the loading-rate dependence of the dynamic fracture toughness. The incubation time to failure of the aircraft aluminum alloy is calculated. The difference in the loading-rate dependences of the dynamic fracture toughness, which is observed for various structural materials, is explained. The dynamic fracture toughness of the alloy under pulsed threshold loads is calculated.

Suppressing nonlinear resonances in an impact oscillator using SMAs

In this paper, we study the resonant responses of an impact oscillator with a one sided SMA motion constraint operating in the pseudoelastic regime. The effectiveness of the SMA restraint in suppressing nonlinear resonances of the impact oscillator is assessed by comparing the dynamic responses of the impact oscillator with SMA and elastic restraints. It is shown that the hysteretic behaviour of the SMA restraint provides an overall vibration reduction in the resonant frequency ranges. Due to the softening behaviour of the SMA element, the resonant frequencies for the SMA oscillator were found to be lower than for the oscillator with an elastic restraint. At each resonance, a single periodic response for the oscillator with the elastic restraint corresponds to two co-existing periodic responses of the SMA oscillator. While at the first resonance peak the emergence of one of the co-existing responses is associated with the hardening effect of the SMA restraint when the pseudoelastic force varies over a complete transformation cycle, at higher frequency resonances incomplete phase transformations in the SMA were detected for both responses. The experimental study undertaken verified the response-modification effects predicted by the numerical analysis conducted under the isothermal approximation. The experimental results showed a good quantitative correspondence with the mathematical modelling.

Anomalous Behavior of Yield Stress upon an Increase in Temperature under High Strain Rate Conditions

The strength characteristics of a material tested under the conditions of short-term high-intensity loading differ substantially as compared with the quasistatic testing data. In addition, effects that cannot be described by classical models are observed. An example of the anomalous behavior of materials under highspeed loading is the increase in the dynamic yield stress of the material upon an increase in temperature described in [1, 2]. It was found in [1] that for strain rates on the order of 5 × 10 5 s ‐1 , the yield stress of highpurity titanium increases with the temperature of the material. An analogous effect was observed in [2] for monocrystalline aluminum. In these experiments, the samples were subjected to the impact action of a plate, leading to the emergence of plane compression waves in the material. The pulse amplitude for titanium in [1] was 4.5‐6.5 GPa, and the temperature of the samples was varied from room temperature to 405‐460 ° C. The yield stresses in monocrystalline aluminum were measured in the temperature range from 15 to 650 ° C, and the pulse amplitude was 5 GPa. To explain such behavior of the material, a new yield criterion was introduced, whose advantage lies in the possibility of simulating the behavior on the material on the basis of a limited number of parameters.

1.18 An Excursion into Representative Volume Elements and Unit Cells

The objective of this chapter is to provide a comprehensive and systematic account on the subject of representative volume elements (RVEs) and unit cells (UCs). To construct an RVE or UC, intuition has been often perceived sufficient to facilitate the analysis, but down to the details, approaches taken turn out to be rather mythological. It will be demonstrated in this chapter that there is absolutely no room for any myth on the subject if the basic concepts of mathematics and mechanics, viz. symmetry and free body diagrams, have been applied correctly and consistently. Only then, effective and reliable means of material characterisation based on the use of RVEs and UCs can be established, in particular, for composites where micro/mesostructures often dictate their behaviours. The logic employed defines the boundary of applicability of the methodology.

Damage related material constants in continuum damage mechanics for unidirectional composites with matrix cracks

Application of a continuum damage mechanics formulation rests on the ease with which the material constants involved in the formulation can be determined. For an initially linear elastic material, the changes in elastic constants induced by damage depend on certain damage related material constants that are commonly determined by experiments in addition to those required to determine the initial properties. This additional experimental task can render the continuum damage mechanics theory less attractive. The present paper will only deal with those associated with damage representation. We propose here a procedure for analytically determining seven out of eight damage related material constants for unidirectional composites assumed initially transversely isotropic and containing a parallel array of matrix cracks along fibres. The remaining constant can be determined experimentally or by a numerical experiment proposed here for the purpose. The analytical expressions derived are in terms of initial elasticity constants of a unidirectional composite and are verified for their accuracy by numerical experiments. Since a unidirectional composite forms a building block in composite laminates, the results obtained here can be naturally used for damage in laminates.