Local Strain State Research Articles

On Parameters Related to Continuous and Discontinuous Recrystallization and Subsequent Grain Growth

Ultra-fine grain structure of less than 5 μm grain size in aluminum and aluminum alloys can be obtained by continuous recrystallization and dynamic recrystallization under different types of deformation such as compression, swaging and cold rolling. The occurrence of continuous recrystallization and dynamic recrystallization is determined by various parameters, mainly by the solute Fe level in the aluminum matrix, but also by the initial grain size, the local strain state, the specific orientation of each individual crystallite and the mis-orientation at the grain boundaries. The subsequent grain growth is greatly affected by these parameters as well as the equilibrium and non-equilibrium segregation of Fe solute to the newly formed grain boundaries, and the interaction of precipitate particles with the migrating grain or subgrain boundaries.

Strain Measurements from Single Grains in Passivated Aluminum Conductor Lines by X-Ray Microdiffraction During Electromigration

AbstractWe describe a method for determining the local strain state of passivated aluminum metal lines from single grains within 2.6 µm × 7.0 µm × 0.75 µm sized regions along the line. X-ray microbeam diffraction is used to obtain localized measurements of thermal and electromigration-induced strain during 37 hours of electromigration in a passivated 2.6 µm-wide, 300 µm-long pure Al conductor line at a current density of 4.2×105 A/cm2 and temperature of 270°C. Diffraction from single grains is used to measure both the in-plane and normal components of strain and their evolution during electromigration at several positions along the line.

Strain-based transient-gradient damage model for failure analyses

A transient-gradient enhanced damage model has been developed for the numerical modelling of the damage and fracture process within a continuum damage mechanics framework. Some deficiencies of existing gradient enhanced damage formulations for the simulation of macroscopic crack propagation are pointed out. The transient-gradient approach assumes a direct coupling between the material length parameter and the local strain state of the material, which leads to a transient behaviour of the nonlocal effect. Details of the method are presented and fully elaborated in an incremental-iterative solution scheme. Mesh objectivity and physical relevance of the method are analysed by one-dimensional and two-dimensional numerical examples.

Flow localization in sheet specimens with pairs of holes

The deformation localization behavior of sheet specimens containing geometric perturbations in the form of pairs of through-thickness holes is examined. Both experiments and computational modeling are performed in either uniaxial or equal-biaxial tension in order to examine the effect of applied loading path on the far-field strain needed to initiate localized necking in the ligament between the hole pairs. The models also examine the influence of hole spacing and matrix strain hardening on ligament localization. The far-field strain needed to cause the localization of the ligament is shown to increase as the biaxiality of the loading path increases, the hole spacing increases, and the strain-hardening exponent increases. The present study also indicates that the onset of localized necking can be predicted by employing the Hill criterion, if the local strain states within the ligament are taken into account.

Modeling piezoceramic actuation of beams in torsion

This paper develops a one-dimensional model to predict the coupled extension, bending and torsion response of a beam subject to piezoceramic strain actuation. The effects of cross-sectional warping are shown to be negligible for thin rectangular isotropic beams. The impact of adhesive shear lag, on the other hand, is measurable, especially in the torsional response. Experimental test results show that the models are accurate up to a 45O actuator orientation with respect to the beam axis even though detailed strain data indicate that the local strain state is highly two-dimensional . Nomenclature

Modelling of the damage in ductile steels

The nucleation, growth and coalescence of voids result in ductile fracture of materials. The first coalescence of voids defines crack initiation. In order to describe the initiation behaviour of a controlled rolled structural steel FeE 460 quantitatively, experimental investigations and micromechanical modelling were conducted. The tests were carried out at room temperature with axisymmetric notched tensile specimens under proportional loading. Specimen geometries containing different notch geometries leading to different stress triaxiality ratios were chosen. Taking into consideration the experimental procedure a failure curve which considers the local state of stress and strain at initiation was evaluated. Different criteria concerning initiation of the ductile failure process by reaching a critical void size R c were proved with regard to the reproduction of the material behaviour.

Phonon behavior and interfacial stress in the strained (InAs) m/(GaAs) n ultrathin superlattices

Phonon behavior in the strained (InAs) m /(GaAs) n ultrathin superlattices grown by molecular beam epitaxy has been investigated by means of Raman scattering spectroscopy. The phonon frequency in the GaAs layers shifts toward lower energy with increasing InAs layer thickness under fixed thickness of GaAs layers. The frequency in the InAs layers does not change significantly, as deduced from the behavior of the InAs-like mode in In xGa 1−xAs alloys. These observed results are phenomenologically discussed on the basis of the combined effect of phonon confinement in the respective layer and stress at the alternating interfaces. Furthermore, a large softening of the phonon confined in the GaAs layers decreases the frequency gap, resulting in traveling of the optical phonons confined in both layers. The strain at the interfaces is estimated by an empirical method, i.e., by comparing the frequency in the superlattice and in the alloy of equivalent composition. In the In xGa 1−xAs alloys, the composition dependence of the mode frequency is considered as being due to the local strain. The group III elements are considered to be in the local strain state from an extended X-ray absorption fine structure (EXAFS) analysis.

A microstructurally based method for stress estimates

A method is described in which quantitative microstructural analysis is used to estimate the local stress and strain states occurring within near-surface layers due to frictional contact. Quantitative estimates of local stress and strain have applications in friction and wear models, in finite element analysis of sliding interfaces, and as a basis for formulating and evaluating models on a local scale. This method is illustrated for three cases of dry sliding on nominally flat surfaces. Sliding tests were performed on a flat plate friction tester, developed at Sandia, which used copper friction samples and a steel test platen. The evolving friction coefficients were measured as a function of normal load and sliding speed. Microstructural analyses included both scanning and transmission electron microscopy (SEM and TEM) of the cross-sectioned friction samples. The sliding-induced dislocation substructures were quantitatively characterized and measured as a function of subsurface depth and normal load. Two simple relationships between the size scale of the dislocation substructure and the flow stress were used to estimate the material properties and the stress state as a function of depth and normal load.

Forging limits for an aluminum matrix composite: Part I. Experimental results

Forging limits in a discontinuously reinforced aluminum (DRA) matrix composite, 2014 Al/15 vol pct A1-2O-3, were determined by compressing samples of various cylindrical geometries under different conditions of temperature, strain rate, and lubrication and measuring the limit strains attained prior to incipient crack formation. In some cases, circumferential grids were machined on the sample surface to obtain the local fracture strain states. Crack formation was caused by the secondary tensile stresses; however, crack propagation was relatively slow and somewhat more severe at 300 °C than at 400 °C. The forging limit of the composite was found to be higher at 400 °C than at 300 °C and also higher at slower strain rates. The plane-strain forging limit of the composite at 300 °C and a strain rate of 0.5 s”1 was less than 0.05, while that of the matrix was higher than 0.5. It was found that the forging limits can be influenced by the depth of the circumferential grids and can be lower than those for the smooth surface samples.

Effect of phase-transformation on mechanical behavior of dual-phase steel plate

The mechanical behavior of dual phase steel plates is affected by internal stresses created during martensite transformation. Analytical modelling of this effect is made by considering a unit cell made of martensite inclusion in a ferrite matrix. A large strain finite element analysis is then performed to obtain the plane stress deformation state. Displayed numerically are the development of the plastic zone and distribution of local state of stress and strain. Studied also are the shape configuration of the martensite (hard-phase) that influences the interfacial condition as related to stress transmission and damage. Internal stresses are found to enhance the global flow stress after yield initiation in the ferrite matrix. Good agreement is obtained between the analytical results and experimental observations.

Experimental and theoretical investigation of the order-disorder transformation in Ni3Al

The crystalline disordered phase obtained by mechanical alloying of elemental 75 at. % Ni and 25 at. % Al powders has been investigated. The stability of this phase with respect to the thermal reordering process leading to the L12 structure has been analyzed by means of x-ray diffractometry, scanning electron microscopy, and differential scanning calorimetry. Atomistic simulations on an Ni3Al model, reproduced via molecular dynamics using a many-body potential, have been used to interpret experimental data. The ordering transformation takes place in an extended range of temperature (from 320 to 600 °C) and occurs simultaneously with the release of internal strain. Numerical simulations performed under different conditions show that the activation energy of the Ni-vacancy migration mechanism responsible for the ordering process depends on the local state of strain, thus suggesting an explanation for the considerable lowering of this energy in samples obtained by ball milling.

On the Applicability of Local Approaches for the Determination of the Failure Behavior of Ductile Steels

The strength and deformation behavior of specimens and components is, on the one hand, influenced by the local state of stress and strain, and on the other hand, by the chemical composition and the microstructure of the material used. Using two different steels, it was investigated how far it is possible to predict the failure behavior of specimens and components qualitatively and quantitatively by means of local approaches. For this purpose, two methods differing considerably from the basic idea were chosen. For the description of the failure behavior, so-called damage models were used. These damage models try to describe numerically the process developing microscopically and finally leading to fracture by means of continuum mechanical approaches in order to calculate the macroscopical failure behavior. The results show that for ductile materials, the damage models allow a very accurate calculation of smooth and notched specimens and components. The efforts presently required for the calculation are, however, still very high. Analyses using fracure mechanics approaches (J-integral) in combination with the local stress states (multiaxiality) were performed to describe the failure behavior. With this approach, it was attempted to calculate crack initiation and maximum load of pre-cracked specimens and components. The fracture mechanics methods are preferred for cracked components if an engineering estimation of crack initiation and maximum load only is required since the calculation efforts of the fracture mechanics methods are much lower than those of the damage models.

A comparison of homogenization and standard mechanics analyses for periodic porous composites

Composite material elastic behavior has been studied using many approaches, all of which are based on the concept of a Representative Volume Element (RVE). Most methods accurately estimate effective elastic properties when the ratio of the RVE size to the global structural dimensions, denoted here as ν, goes to zero. However, many composites are locally periodic with finite ν. The purpose of this paper was to compare homogenization and standard mechanics RVE based analyses for periodic porous composites with finite ν. Both methods were implemented using a displacement based finite element formulation. For one-dimensional analyses of composite bars the two methods were equivalent. Howver, for two- and three-dimensional analyses the methods were quite different due to the fact that the local RVE stress and strain state was not determined uniquely by the applied boundary conditions. For two-dimensional analyses of porous periodic composites the effective material properties predicted by standard mechanics approaches using multiple cell RVEs converged to the homogenization predictions using one cell. In addition, homogenization estimates of local strain energy density were within 30% of direct analyses while standard mechanics approaches generally differed from direct analyses by more than 70%. These results suggest that homogenization theory is preferable over standard mechanics of materials approaches for periodic composites even when the material is only locally periodic and ν is finite.

Strain localization behaviour in experimental shear zones

A torsional deformation apparatus has been developed which allows the evolution of microstructures and flow patterns in analogue materials to be observed to shear strains in excess of γ=100 while the loading conditions are kept constant. Using a computer-based video microscopy system the displacement paths of marker particles have been followed in real time, and from these the local strain states in the samples have been calculated. A series of velocity stepping experiments in octachloropropane and norbornene determined the shear localization behaviour displayed by these materials. Both of these materials underwent two phases of localization, a primary localization at the start of an experiment, and a secondary localization following increases in the imposed strain rate. The secondary localization is less pronounced, but is reversible, in the sense that lowering the imposed strain rate widens the zone. An inverse relationship between the fixed imposed strain rate and the width of the zone of localized deformation was established. This velocity dependant localization is ascribed to the softening effect of dynamic recrystallization.

Control of intergranular fatigue cracking by slip homogeneity in copper: II. Effect of loading mode: Liang, F.-L. and Laird, C. Mater. Sci. Eng. A Sept. 1989 A117, (1–2), 103–113

The effect of local strain state on twinning behavior during compression of AZ31 magnesium alloy was investigated, making use of a micro-grid method to correlate the local strain tensor with observations of twinning using electron backscatter diffraction (EBSD) measurements. Eight prism samples were used to get deformation zones subjected to different strain states. The strain distribution across the whole sample surface was measured with the micro-grid method and the results show that the local strain states exhibit much variation, with zones subjected to large shear strain as well as zones subjected to little shear strain. Samples were compressed at room temperature and detailed EBSD measurements were taken in two zones, where one zone was subject to only small shear strains and the other was subject to large shear strains. Twin variant selection was then analyzed with respect to both stress-based (Schmid factor) and strain-based criteria. The former was found to provide the best explanation for the observed pattern of twinning.

Nonlinear Behavior of Elastomeric Bearings. II: FE Analysis and Verification

A “composite,” three-dimensional finite element analysis based on an “equivalent homogeneous continuum” model for the nonlinear behavior of a class (flat layers) of elastomeric bearings is developed. The analysis may also find application for other layered composites that exhibit the fundamental behavior characteristics of elastomeric bearings. The developed “composite” finite element analysis is far less expensive than the alternative of using a general purpose finite element program to perform “discrete” analyses of elastomeric bearings. The analysis not only calculates the overall (average) response of bearings but yields predictions of the local stress and strain states that exist within individual layers of bearings. Both geometric and material nonlinearities are included in the analysis. The analysis (and underlying theory) are “verified” by making comparisons of the finite element predictions to results from discrete analyses of simple configurations and to experimental measurements of actual bearing behavior.

Nolinear Behavior of Elastomeric Barings. I: Theory

An “equivalent homogeneous continuum” theory for the nonlinear behavior of a class (flat layers) of elastomeric bearings is developed. The theory should also find application for other layered composites that exhibit the fundamental behavior characteristics of elastomeric bearings. The theory models not only the average behavior of the bearings, but also the important edge effects that significantly affect many of the response characteristics of this class of layered solids. For this purpose, in addition to the displacement unknowns, edge effect field variables are introduced into the model. The theory not only permits the calculation of the overall (average) response of bearings, but yields estimates of the local stress and strain states that exist within their individual layers. Both geometric and material nonlinearities are included in the model. While in theory the model could be used to generate analytical solutions for bearing behavior, it is primarily intended as a foundation from which to develop a “composite” finite element analysis for elastomeric bearings. Such a composite analysis is far less expensive than the alternative of using a general purpose finite element program to perform “discrete” analyses of elastomeric bearings.

Plastic near-tip fields for branched cracks

A procedure is outlined whereby the plastic near-tip stress and deformation fields for branched cracks are determined under plane strain and small scale yielding conditions. This method utilizes the known elastic stress intensity factor solutions and the universal mixed-mode plastic near-tip fields to determine the stress and deformation conditions at the tip of a kinked or forked crack. The plastic near-tip fields are characterized by an amplitude and a mixity parameter. We examine the influence of crack tip plasticity and material strain hardening characteristics on the local stress and strain states. Possible beneficial effects of crack branching and crack tip plasticity on fracture toughness and crack growth resistance are discussed in the light of these results.