An alternative approach to state estimation in linear time-invariant systems

An alternative approach to state estimation problem in linear, time-invariant dynamic systems is presented in this paper. The approach developed first identifies the initial state of the system by using a proportional plus integral parameter identification method. The Lyapunov design technique is used to guarantee the asymptotic convergence of the initial state identifier. A state estimator is then constructed to operate in series with the initial state identifier. The estimator generates an estimate of the unobserved part of the system state. Simulation studies have shown that satisfactory state estimation can be achieved in the presence of measurement or disturbance noise. An example problem is considered to demonstrate the response characteristics of the estimator-identifier combination.     

The effect of twinning and slip on the bauschinger effect of hadfield steel single crystals

The Bauschinger effect (BE) in single crystals of Hadfield manganese steel (Fe, 12.3Mn, 1.0C in wt pct) was studied for three crystallographic orientations, , and [001]. Both forward tension-reverse compression (FT/RC) and forward compression-reverse tension (FC/RT) loading schemes were used to investigate the role of deformation history on the BE. The evolution of stress-strain response and a dimensionless Bauschinger parameter were used to study the BE. The BE stems from long-range back stress generated by the dislocation pileups at the twin and localized slip boundaries. Twinning boundaries present a strong obstacle and lead to a strong BE. If localized slip followed twinning, permanent softening was evident, such as in the case of the FT/RC scheme. Localized slip and multiple slip in the forward loading provided a transient effect in the stress-strain response without a significant permanent softening. Hadfield steel single crystals have demonstrated a high BE for orientations conducive to combined twinning/slip deformation. The BE increased with increasing prestrain, then saturated and started to decrease, in contrast with precipitation-hardened alloys. A unique strain-hardening approach along with the back stress calculation was introduced into a viscoplastic self-consistent (VPSC) formulation. The strain-hardening formulation incorporates length scales associated with spacing between twin lamellae. The simulations correctly predicted the BE and the stress-strain response for both forward and reverse loading.     

The deformation of low-stacking-fault-energy austenitic steels

As nanostructured materials advance, their potential for applications to everyday life grows. Austenitic steels with low-stacking-fault energy, which experience twinning as a primary deformation mechanism leading to nanoscale layered structures, can be classified in this group of materials. This overview summarizes recent experimental findings and modeling efforts to determine how these nanostructures and microstructures affect mechanical response and texture evolution.     

Precipitate effects on the mechanical behavior of aluminum copper alloys: Part I. Experiments

This article focuses on understanding the mechanical behavior of precipitation-hardened alloys by studying single and polycrystalline deformation behavior with various heat treatments. Aluminumcopper alloys are the focus in this work and their changing stress-strain behavior is demonstrated resulting from the different hardening mechanisms brought about by the various precipitates. Extensive transmission electron microscopy investigations facilitated the interpretation of the stress-strain behavior and the work hardening characteristics. The use of both single and polycrystals proved valuable in understanding the role of anisotropy due to crystal orientation vs precipitate-induced anisotropy. The experiments show that precipitation-induced anisotropy could offset the crystal orientation anisotropy depending on the orientation. This is clearly demonstrated with similar [111] and [123] behaviors under 190 °C and 260 °C aging temperatures. Experiments on pure aluminum crystals are also provided for comparison and understanding the crystal anisotropy in the absence of precipitates. Part I of this article will focus on experiments, and part II will describe the modeling of the effect of different metastable phases in the matrix acting as barriers to dislocation motion.     

The role of nitrogen on the deformation response of hadfield steel single crystals

We studied the role of nitrogen content on the stress-strain response of Hadfield steel (HS) single crystals under compressive loading. Two different nitrogen concentrations were examined for each orientation (0.05 wt pct and 1.06 wt pct) with drastic increase in critical resolved shear stresses (CRSSs) and strain-hardening coefficients compared to HS without nitrogen. The stress-strain response was strongly dependent on both the crystallographic orientation and the nitrogen concentration. Transmission electron microscopy (TEM) results revealed that, for the HS with 1.06 wt pct nitrogen, the hardening is influenced by the coexisting deformation twins and precipitates, which both act as strong obstacles against dislocation motion. A visco-plastic self-consistent (VPSC) model was modified to account for precipitation and twinning length scales in HS with 1.06 wt pct nitrogen for selected crystallographic orientations. Incoherent precipitates in the hardening formulation were treated as factors affecting the mean free path of dislocations. The model also accounts for plastic relaxation of precipitates with increasing strain and accurately predicts the stress-strain response.     

Plastic zones and fatigue-crack closure under plane-strain double slip

The results of a systematic investigation involving forward and reversed plastic zones for a growing fatigue crack under plane-strain double-slip conditions are presented. The study focuses on plastic-deformation fields outside the small-scale yielding regime. The size of the macroscopic forward plastic zone is found to be nearly proportional to the square of the applied-stress intensity over the critical resolved shear stress. The size of the forward plastic zone is also found to depend on the angles of the two microscopic slip directions with respect to the crack line. When the microscopic slip directions are kept symmetric about the crack-line normal, and the angle between them is varied, the forward plastic zone sizes hardly vary. However, when the angle between the slip lines is kept constant, and both planes are simultaneously rotated, the forward plastic zone sizes vary by a factor of three. The ratio of the reversed plastic zone size to the forward plastic zone size is also found to be dependent on the orientation of the microscopic slip planes. The ratio varies when the angle between the microscopic slip planes is changed, or when the orientations of both planes are rotated simultaneously. Stationary cracks are generally found to have larger reversed plastic zones than fatigue cracks, and the difference is attributed to crack closure.     

Fracture of precipitated NiTi shape memory alloys

The fracture mechanisms in single crystal and polycrystalline Ti-50.8at%Ni shape memory alloys containing Ti₃Ni₄ precipitates are studied using the scanning electron microscope (SEM). Aged materials with three different precipitate sizes (50 nm, 150 nm, and 400 nm), which have interfaces ranging from semi-coherent to incoherent, are considered. The mechanisms of material fracture identified in the single crystal NiTi are: 1. Nucleation, growth, and coalescence of voids from the Ti₃Ni₄ precipitates, 2. Cleavage fracture on {100} and {110} crystallographic planes, 3. Nucleation, growth, and coalescence of voids from fractured Ti-C inclusions. Cleavage and ductile tearing mechanisms also operate in polycrystalline NiTi, however, since the Ti-C inclusions are an artifact of single crystal growth processes, mechanism 3 was not discovered in the polycrystalline materials. Cleavage fracture and ductile tearing are found to act in conjunction, with the relative dominance of one over the other depending on the local precipitate size and concentration. As the Ti₃Ni₄ precipitate size increases to about 400 nm, the overall fracture is dominated by failure mechanism 1, and the cleavage markings become diffuse. Finally, we assert that the high tensile ductility of drawn NiTi polycrystals is due partially to the fact that drawn bar and wire stock usually have a strong {111} fiber texture. Such a texture promotes the initiation of the transformation at low stresses and concurrently prevents primary cleavage on the {100} or {110} planes.     

Contact of crack surfaces during fatigue: Part 1. formulation of the model

A model has been developed to predict crack opening and closing behavior for propagating fatigue cracks which undergo significant sliding displacements at crack flanks. Crack surfaces were described statistically by assuming a random distribution of asperity heights and a mean density of asperities and asperity radii. The propagating crack was subdivided into strips, and each strip was treated as a contact problem between two randomly rough surfaces. The remote tensile stresses were varied in a cyclical manner. The contact stresses at minimal load were determined by analyzing the local crushing of asperities via a sliding mechanism. Then, upon loading, the crack opening stress levels were computed when the contact stresses were overcome. Part 1 of this article includes a discussion of the previous models, then introduces statistical contact mechanics concepts which are utilized in the fatigue crack growth simulations. In addition, the numerical algorithms for the modeling work and the sensitivity of results to model parameters are described. The role of stress ratio, maximum stress level, crack length, and the geometry of crack surfaces on the crack growth behavior will be discussed in Part 2 of this article.