Relating inhomogeneous deformation to local texture in zirconium through grain-scale digital image correlation strain mapping experiments

The effect of local texture on inhomogeneous plastic deformation is studied in zirconium subjected to uniaxial compression. Cross-rolled commercially pure Zr 702 plate that had a strong basal (0 0 0 1) texture through the plate thickness, and a non-basal texture in cross-section, was obtained. At a compressive strain rate of 1 s^?1, samples loaded either in the through-thickness or in-plane directions exhibited significant differences in yield strength, hardening response and failure mechanisms. These macroscopic differences are related to microstructural features by combining information from electron backscattered diffraction with real time in situ imaging and subsequent full-field strain measurements obtained using digital image correlation. Experimental results indicate that the through-thickness loaded zirconium samples, which show a strong basal-texture in the loading direction, do not deform homogeneously – implying the lack of a representative volume element. The detailed surface deformation fields provided by digital image correlation allow for a qualitative and quantitative analysis of the relationship between grain orientation and patterns of deformation bands that form as the precursors to development of an adiabatic shear band in the through-thickness loaded sample. For the in-plane loaded samples, inhomogeneities still exist at the microscale, but the collective behavior of several grains leads to a homogeneous response at the macroscale. It is observed that local texture for hcp polycrystals, which are significantly slip restricted, can directly affect both local and global response, even at low to moderate plastic strains.     

Analysis of deformation-induced crack tip toughening in ductile single crystals by nano-indentation

This paper reports on the experimental examination of the deformation characteristics near a crack tip in a cyclically work-hardened copper single crystal using a 2D surface scans with nano-indentation. The experimental methodology enables the characterization of the primary deformation field near a crack tip via the modulation of the imposed secondary deformation field by a nano-indentation. In a heavily deformed 4-point bend specimen, the measurements showed an existence of an asymptotic field around the crack tip at a distance of R ⩾ 2.5J/σ₀. The measurements also showed the qualitative details of toughness evolution within the high-gradient deformation field around the crack tip. The nature of dislocation distribution (i.e. statistically distributed vs. distributions necessitated by geometry) around the crack tip is quantified. The measurements indicate the dominance of the geometrically necessary dislocation within the finite deformation zone ahead of the tip up to a distance of R ≈ 3J/σ₀. Thereafter, it is confined in radial rays coinciding with the sector boundaries around the crack tip. These measurements elucidate the origin of the inhomogeneous hardening and the size dependent macroscopic response close to crack tip.     

Characterization and modelling of a carbon ramming mix used in high-temperature industry

This paper is devoted to the modelling of a specific ramming mix mainly used in the high-temperature industry due to its high-compacting behaviour. This material has the ability to absorb the deformation of parts submitted to high thermal loads. Triaxial and instrumented die compaction tests were carried out in order to identify the shear and hardening behaviours, respectively. Tests on the ramming mix were led for a temperature range between 20 °C and 80 °C. The temperature effect is particularly observed on the material response when it is compacted. The main features of the behaviour of the ramming mix can be represented by the theoretical framework of the Modified Cam-Clay model. A single variable allows to accurately reproduce the hardening behaviour depending on the temperature. Moreover, an extension of the model for the hardening behaviour at high pressures is proposed. A good agreement between the experimental data and numerical tests is reached with this model.     

A 1-D theory for extensional deformation of a viscoelastic filament under exponential stretching

We consider a viscoelastic filament placed between two coaxial discs, with the bottom plate fixed and the top plate pulled at an exponential rate. Using a slender rod approximation, we derive a one-dimensional (1-D) model which describes the deformation of a viscoelastic filament governed by the Oldroyd-B constitutive model. It is assumed that the flow is axisymmetric and that inertia and gravity are negligible. One solution of the model equations corresponds to ideal uniaxial elongation. A linear stability analysis shows that this solution is unstable for a Newtonian fluid and for viscoelastic filaments with small Deborah number (De ≤ 0.5). For Deborah number greater than 0.5, ideal uniaxial elongation is linearly stable. Numerical solution of the nonlinear equations confirms the result of the linear stability analysis. For initial conditions close to ideal uniaxial flow, our results show that if De > 0.5, the central portion of the filament undergoes considerable strain hardening. As a result, the sample remains almost cylindrical and the deformation approaches pure uniaxial extension as the Hencky strain increases. For De ≤ 0.5, the Trouton ratio based on the effective extension rate at the mid-plane radius gives a much better approximation to the true extensional viscosity than that based on the imposed stretch rate.     

On the strain hardening and texture evolution in high manganese steels: Experiments and numerical investigation

We present a systematic investigation on the strain hardening and texture evolution in high manganese steels where twinning induced plasticity (TWIP) plays a significant role for the materials' plastic deformation. Motivated by the stress–strain behavior of typical TWIP steels with compositions of Fe, Mn, and C, we develop a mechanistic model to explain the strain-hardening in crystals where deformation twinning dominates the plastic deformation. The classical single crystal plasticity model accounting for both dislocation slip and deformation twinning are then employed to simulate the plastic deformation in polycrystalline TWIP steels. While only deformation twinning is activated for plasticity, the simulations with samples composed of voronoi grains cannot fully capture the texture evolution of the TWIP steel. By including both twinning deformation and dislocation slip, the model is able to capture both the stress–strain behaviors and the texture evolution in Fe–Mn–C TWIP steel in different boundary-value problems. Further analysis on the strain contributions by both mechanisms suggests that deformation twinning plays the dominant role at the initial stage of plasticity in TWIP steels, and dislocation slip becomes increasingly important at large strains.     

Coupled annealing temperature and layer thickness effect on strengthening mechanisms of Ti/Ni multilayer thin films

A systematic study was performed on mechanical and microstructural properties of Ti/Ni multilayers with layer thickness from 200 nm to 6 nm and annealing temperature from room temperature to 500 °C. Based on the observed hardness evolution, a coupled layer-thickness and annealing-temperature dependent strengthening mechanism map is proposed. For as-deposited films, the deformation behavior follows the traditional trend of dislocation mediated strengthening to grain boundary mediated softening with decreasing layer thickness. For annealed films, grain boundary relaxation is considered to be the initial strengthening mechanism with higher activation temperature required for thicker layers. Under further annealing, solid solution hardening, intermetallic precipitation hardening, and fully intermixed alloy structure continue to strengthen the thin layered films, while recrystallization and grain-growth lead to the eventual softening of thick layered films. For the films with intermediate layer thickness, a strong orientation dependent hardness behavior is exhibited under high temperature annealing due to mechanism switch from grain growth softening to intermetallic precipitation hardening when changing the loading orientation from perpendicular to parallel to the layer interfaces.     

Complex investigation of deformation twinning in γ-TiAl by TEM and neutron diffraction

A near-γ TiAl based alloy with 2 at% of Nb was investigated by means of collaborative research based on transmission electron microscopy and in-situ neutron diffraction techniques with the aim to study mechanical twinning and its role within the mechanisms governing fatigue response and material properties. In-situ neutron diffraction measurements were performed during low cycle fatigue straining at room temperature. Induced lattice strain related to the formation of deformation twins was detected and used to follow changes in the macroscopic material response caused by the twinning process during cycling. A microscopic insight was realised by using several transmission electron microscopy techniques to reveal in detail an internal deformation microstructure of the material at the beginning as well as at the end of the fatigue life. The study was focused on the first loading cycles where the material shows intense cyclic hardening. The effect of mechanical twinning on the material behaviour at several stages of the fatigue life is discussed for two different total strain amplitudes of 0.2% and 0.4%.     

An experimental and numerical study of the localization behavior of tantalum and stainless steel

In general, the shear localization process involves initiation and growth. Initiation is expected to be a stochastic process in material space where anisotropy in the elastic–plastic behavior of single crystals and inter-crystalline interactions serve to form natural perturbations to the material’s local stability. A hat-shaped sample geometry was used to study shear localization growth. It is an axi-symmetric sample with an upper “hat” portion and a lower “brim” portion with the shear zone located between the hat and brim. The shear zone length is 870–890 μm with deformation imposed through a split-Hopkinson pressure bar system at maximum top-to-bottom velocity in the range of 8–25 m/s. We present experimental results of the deformation response of tantalum and 316L stainless steel samples. The tantalum samples did not form shear bands but the stainless steel sample formed a late stage shear band. We have also modeled these experiments using both conductive and adiabatic continuum models. An anisotropic elasto-viscoplastic constitutive model with damage evolution was used within the finite element code EPIC. A Mie-Gruneisen equation of state and the rate and temperature sensitive MTS flow stress model together with a Gurson flow surface were employed. The models performed well in predicting the experimental data. The numerical results for tantalum suggested a maximum equivalent strain rate on the order of 7 × 10⁴ s⁻¹ in the gage section for an imposed top surface displacement rate of 17.5 m/s. The models also suggested that for an initial temperature of 298 K a temperature in the neighborhood of 900 K was reached within the shear section. The numerical results for stainless steel suggest that melting temperature was reached throughout the shear band shortly after peak load. Due to sample geometry, the stress state in the shear zone was not pure shear; a significant normal stress relative to the shear zone basis line was developed.     

Simple constitutive modelling of nonlinear viscoelasticity under general extension

We study the behaviour of a single integral constitutive equation, capable of providing analytic expressions for the viscoelastic stress in extensional flows of a variety of deformation histories and geometries, ranging from uniaxial to equibiaxial. It is based on the use of a stress damping function, with a power-law dependence on the elongation, λ: h(λ) = 1/λⁿ. The parameter n (0 ≤ n ≤ 2) signifies the nonlinear viscoelastic character of the material and, therefore, is an inverse measure of network connectivity strength of the underlying microstructure. This renders the constitutive approach applicable to incompressible polymers of a variable degree of branching, strain hardening and stress thinning behavior. Methods of connecting n with the macromolecular architecture and the alignment strength of the flow are also explored.     

A dislocation-based constitutive law for pure Zr including temperature effects

In this work, a single crystal constitutive law for multiple slip and twinning modes in single phase hcp materials is developed. For each slip mode, a dislocation population is evolved explicitly as a function of temperature and strain rate through thermally-activated recovery and debris formation and the associated hardening includes stage IV. A stress-based hardening law for twin activation accounts for temperature effects through its interaction with slip dislocations. For model validation against macroscopic measurement, this single crystal law is implemented into a visco-plastic-self-consistent (VPSC) polycrystal model which accounts for texture evolution and contains a subgrain micromechanical model for twin reorientation and morphology. Slip and twinning dislocations interact with the twin boundaries through a directional Hall–Petch mechanism. The model is adjusted to predict the plastic anisotropy of clock-rolled pure Zr for three different deformation paths and at four temperatures ranging from 76 K to 450 K (at a quasi-static rate of 10⁻³ 1/s). The model captures the transition from slip-dominated to twinning-dominated deformation as temperature decreases, and identifies microstructural mechanisms, such as twin nucleation and twin–slip interactions, where future characterization is needed.     

The contribution of small leaks in a baghouse filter to dust emission in the PM2.5 range—A system approach

The contribution of leakage in a baghouse filter (defined as a short circuit between the upstream and downstream sides of the filter) to the emission of fine particles is quantified in comparison to other dust emission sources, and the influence of key operating variables on overall system response is analyzed. The study was conducted on a well-maintained pilot-scale filter unit (9 bags of 500 g/m² calendered polyester needle felt; total surface area 4.2 m²) operated in Δp-controlled mode over a range of pulsing intensities, with two types of test dust (one free-flowing and the other cohesive) at inlet concentrations of 10 and 30 g/m³. Leaks included single holes between 0.5 and 4 mm diameter, intentionally placed in either the plenum plate or one of the filter bags, as well as seamlines from bag confectioning. Emissions were separated by source into a transient contribution due to dust penetration through the filter bags after each cleaning pulse, and a continuous contribution from leaks. This separation was based on a novel method of data processing that relies on time-resolved concentration measurements with a specially calibrated optical particle counter. Tiny leaks on the order of 1 mm generated the same emission level as all the bags combined, and dominated continuous emissions. The equivalent leak cross section (leakage = media emission) was about 1 ppm of the total installed filter surface, independent of upstream dust concentration. Leakage through open seamlines amounted to 75% of media emissions in case of free-flowing test dust. Leakage was restricted to aerodynamic diameters less than ∼5 μm (roughly the PM_2.5 mass fraction). For comparison, time-averaged mass penetration through conventional needle-felt media ranged from about 10⁻⁵ to 10⁻⁶, depending on cohesiveness of the particle material and pulse cleaning intensity, giving emission levels between about 0.02 and 0.2 mg/m³ at the reference concentration of 10 g/m².     

New investigations on transformation induced plasticity and its interaction with classical plasticity

In this paper, transformation induced plasticity (TRIP) in anisothermal single as well as double transformations (austenite → bainite and austenite → bainite + Martensite) in 16MND5 steel is experimentally analyzed. Several investigations have been performed related mainly on: (a) the evaluation of the physical mechanism responsible of the TRIP in bainitic transformation; (b) the kinetics of TRIP and its specificity in a double transformation; (c) the consequence when the load is applied during only a part of phase transformation; (d) the interaction between TRIP and classical plasticity and so on. The results seem indicate that Greenwood and Johnson mechanism is dominant compared to Magee mechanism. The interaction between classical plasticity and TRIP is clearly demonstrated and it seems that the strain hardening state of the parent phase plays an important role in the TRIP progress. Due to such interaction, TRIP appears even in the absence of external applied load; the behavior depends strongly on the transformation under consideration (bainitic or martensitic). From a modeling point of view, it is shown that Leblond’s model that is the only one “industrial” model which enables qualitatively to account for such interactions, fails to predict the observed phenomena especially in martensitic transformation.     

Effect of elastic anisotropy on surface pattern evolution of epitaxial thin films

Stress-induced surface instability and evolution of epitaxial thin films leads to formation of a variety of self-assembled surface patterns with feature sizes at micro- and nanoscales. The anisotropy in both the surface and bulk properties of the film and substrate has profound effects on the nonlinear dynamics of surface evolution and pattern formation. Experimentally it has been demonstrated that the effect of anisotropy strongly depends on the crystal orientation of the substrate surface on which the film grows epitaxially. In this paper we develop a nonlinear model for surface evolution of epitaxial thin films on generally anisotropic crystal substrates. Specifically, the effect of bulk elastic anisotropy of the substrate on epitaxial surface pattern evolution is investigated for cubic germanium (Ge) and SiGe films on silicon (Si) substrates with four different surface orientations: Si(0 0 1), Si(1 1 1), Si(1 1 0), and Si(1 1 3). Both linear analysis and nonlinear numerical simulations suggest that, with surface anisotropy neglected, ordered surface patterns form under the influence of the elastic anisotropy, and these surface patterns clearly reflect the symmetry of the underlying crystal structures of the substrate. It is concluded that consideration of anisotropic elasticity reveals a much richer dynamics of surface pattern evolution as compared to isotropic models.     

Measurement method of complex viscoelastic material properties

A measurement technique of viscoelastic properties of polymers is proposed to investigate complex Poisson’s ratio as a function of frequency. The forced vibration responses for the samples under normal and shear deformation are measured with varying load masses. To obtain modulus of elasticity and shear modulus, the present method requires only knowledge of the load mass, geometrical characteristics of a sample, as well as both the amplitude ratio and phase lag of the forcing and response oscillations. The measured data were used to obtain the viscoelastic properties of the material based on a 2D numerical deformation model of the sample. The 2D model enabled us to exclude data correction by the empirical form factor used in 1D model. Standard composition (90% PDMS polymer + 10% catalyst) of silicone RTV rubber (Silastic^® S2) were used for preparing three samples for axial stress deformation and three samples for shear deformation. Comprehensive measurements of modulus of elasticity, shear modulus, loss factor, and both real and imaginary parts of Poisson’s ratio were determined for frequencies from 50 to 320 Hz in the linear deformation regime (at relative deformations 10^?6 to 10^?4) at temperature 25 °C. In order to improve measurement accuracy, an extrapolation of the obtained results to zero load mass was suggested. For this purpose measurements with several masses need to be done. An empirical requirement for the sample height-to-radius ratio to be more than 4 was found for stress measurements. Different combinations of the samples with different sizes for the shear and stress measurements exhibited similar results. The proposed method allows one to measure imaginary part of the Poisson’s ratio, which appeared to be about 0.04–0.06 for the material of the present study.     

Plastic anisotropy and the role of non-basal slip in magnesium alloy AZ31B

Mechanistic explanations for the plastic behavior of a wrought magnesium alloy are developed using a combination of experimental and simulation techniques. Parameters affecting the practical sheet formability, such as strain hardening rate, strain rate sensitivity, the degree of anisotropy, and the stresses and strains at fracture, are examined systematically by conducting tensile tests of variously oriented samples at a range of temperatures (room temperature to 250 °C) and strain rates (10⁻⁵–0.1 s⁻¹). Polycrystal plasticity simulations are used to model the observed anisotropy and texture evolution. Strong in-plane anisotropy observed at low temperatures is attributed to the initial texture and the greater than anticipated non-basal cross-slip of dislocations with 〈a〉 type Burgers vectors. The agreement between the measured and simulated anisotropy and texture is further validated by direct observations of the dislocation microstructures using transmission electron microscopy. The increase in the ductility with temperature is accompanied by a decrease in the flow stress, an increase in the strain rate sensitivity, and a decrease in the normal anisotropy. Polycrystal simulations indicate that an increased activity of non-basal, 〈c + a〉, dislocations provides a self-consistent explanation for the observed changes in the anisotropy with increasing temperature.     

Study of a drawing-quality sheet steel. II: Forming-limit curves by experiments and micromechanical simulations

In Part I of the current paper, we showed the results of uniaxial-tension tests, through-thickness and plane-strain compression experiments, quantitative texture – orientation distribution function – evaluations and Lankford coefficient measurements. These data were used for calibration and verification of a visco-plastic self-consistent (VPSC) polycrystal-plasticity simulation code for predicting a steel sheet’s ability to be stretched and deep drawn. Lankford coefficients are one, although incomplete, measure of a steel’s drawing quality. In order to obtain a deeper insight and better verification of the simulation code, we measured the forming-limit curve, FLC, for the same steel sheet. To make these measurements we stretched circle-gridded sheets of material with a punch and die. Samples had both a flat-sided and hourglass geometry and ranged from 20 to 80 mm in width. The 80 mm wide sample completely filled the die. With this range of sample sizes, we spanned all of the stress states applicable to a FLC, from uniaxial to biaxial tension. Our FLC curve had the classic “V” shape typical of drawing-quality steel, with a minimum safe forming strain of about 0.35 in plane-strain deformation and a safe forming strain of nearly 0.45 in balanced biaxial stretching. To model the FLC behavior, we used the same VPSC model and calibration employed in Part I. In order to obtain a necking instability in the calculation, a Marciniak defect was implemented into the VPSC model. The severity of the defect was adjusted to match the measured instability strain, 0.35, in plane-strain deformation. Both hardening laws fit in Part I were used to calculate the FLC. In the positive biaxial quadrant of the FLC, the limit strains predicted by the power law closely follow the measured uniform deformations, while the saturation law appears to over predict the limit strains. In uniaxial-tension, it was the opposite. The power-law hardening predictions seemed excessive. However, if we consider the FLC curve to be a band of finite width, both hardening laws and the VPSC formulation capture the essence of the FLC data.     

Thermo-mechanical response of nylon 101 under uniaxial and multi-axial loadings: Part I,Experimental results over wide ranges of temperatures and strain rates

A comprehensive study of the thermo-mechanical response of a thermoplastic polymer, nylon 101 is presented. Quasi-static and dynamic compression uniaxial and multi-axial experiments (stress states) were performed at a wide range of strain rates (10⁻⁵ to 5000 s⁻¹) and temperatures (−60 to 177 °C or −76 to 350 °F). The material is found to be non-linearly dependent on strain rate and temperature. The change in volume after plastic deformation is investigated and is found to be negligibly small. The relaxation and creep responses at room temperature are found to be dependent on strain rate and the stress–strain level at which these phenomena are initiated. Total deformation is decomposed into visco-elastic and visco-plastic components; these components have been determined at different levels of deformation. Results from non-proportional uniaxial to biaxial compression, and torsion experiments, are also reported for three different strain rates at room temperature. It is shown that nylon 101 has a response dependent on the hydrostatic pressure.     

Dynamic response of tubular dielectric elastomer transducers

In this paper, a numerical model for the dynamic response of tubular dielectric elastomer transducers is presented and validated with experimental results for the first time. Dielectric elastomers (DE) are soft polymer based smart materials that can be potentially employed in applications such as actuation, sensing and energy harvesting (Kornbluh, 2004, Carpi et al., 2005, Waki et al., 2008). In our previous work, the quasi-static response of tubular DE transducers was studied (Goulbourne et al., 2007, Son and Goulbourne, 2009). Here, a numerical model is developed to predict the dynamic response of tubular DE transducers. Inertia effects are included in our previous static model which yields a system of partial differential equations. The results of the dynamic response of the tubular DE transducers are obtained by numerically solving the simplified partial different equations using a finite difference scheme. The capacitance change induced by the dynamic deformation of the tubular DE is also calculated by a simple electrostatic model, illustrating dynamic passive sensing.Several tubular DE transducer samples (VHB 4905 and silicone) were fabricated and an experimental setup was developed to investigate the dynamic response by measuring capacitance and radial deformation. In the sensing experiments, a sweep of dynamic pressure profiles (0–5 Hz) are applied. It is observed that silicone transducers have a larger dynamic sensing range. In the actuation experiments, the deformation of the silicone actuator is monitored while a voltage signal (4.5 kV) is applied from 0 to 30 Hz. The silicone actuator shows a good actuation response. The comparison between numerical and experimental results for the DE transducers shows an overall error of 3%.     

Asymptotic crack-tip fields for dynamic crack growth in compressive power-law hardening materials

The effect of material compressibility on the stress and strain fields for a mode-I crack propagating steadily in a power-law hardening material is investigated under plane strain conditions. The plastic deformation of materials is characterized by the J₂ flow theory within the framework of isotropic hardening and infinitesimal displacement gradient. The asymptotic solutions developed by the present authors [Zhu, X.K., Hwang K.C., 2002. Dynamic crack-tip field for tensile cracks propagating in power-law hardening materials. International Journal of Fracture 115, 323–342] for incompressible hardening materials are extended in this work to the compressible hardening materials. The results show that all stresses, strains, and particle velocities in the asymptotic fields are fully continuous and bounded without elastic unloading near the dynamic crack tip. The stress field contains two free parameters σ_eq0 and s₃₃₀ that cannot be determined in the asymptotic analysis, and can be determined from the full-field solutions. For the given values of σ_eq0 and s₃₃₀, all field quantities around the crack tip are determined through numerical integration, and then the effects of the hardening exponent n, the Poisson ratio ν, and the crack growth speed M on the asymptotic fields are studied. The approximate behaviors of the proposed solutions are discussed in the limit of ν → 0.5 or n → ∞.