Mark A. Iadicola

Rate and thermal sensitivities of unstable transformation behavior in a shape memory alloy

A special plasticity-based constitutive model with an up–down–up flow rule used within a finite element framework has previously been shown to simulate the inhomogeneous nature and the thermo-mechanical coupling of stress-induced transformation seen in a NiTi shape memory alloy. This paper continues this numerical study by investigating the trends of localized nucleation and propagation phenomena for a wider range of loading rates and ambient thermal conditions. Local self-heating (due to latent heat of transformation), the inherent Clausius–Clapeyron relation (sensitivity of the materials transformation stress with temperature), the size of the specimens nucleation barriers, the loading rate, and the nature of the ambient environment all interact to create a variety of mechanical responses and transformation kinetics. The number of transformation fronts is shown to increase dramatically from a few fronts under nearly isothermal conditions to numerous fronts under nearly adiabatic conditions. A non-dimensional film coefficient and non-dimensional conductivity are identified to be the major players in the range of responses observed. It is shown that the non-dimensional film coefficient generally determines the overall temperature response, and therefore force–displacement response, of a transforming specimen; whereas, the non-dimensional conductivity is the more important player in determining the number of nucleations, and therefore the number of transformation fronts, that may occur.

The effect of uniaxial cyclic deformation on the evolution of phase transformation fronts in pseudoelastic NiTi wire

Experiments are presented of the response of pseudoelastic NiTi wires subjected to displacement controlled cycles. A custom-built thermo-mechanical testing apparatus is used to control the background temperature field of the wire specimen while allowing the evolution of transformation fronts to be tracked by full-field infrared imaging. Two experiments under similar end-displacement histories, but at temperatures approximately 8°C apart, are shown to give remarkably different cyclic responses. The mechanical response for the lower temperature experiment continued to soften but retained its shape through 43 partial transformation cycles, and the pattern of transformation fronts seemed to reach a steady state. The response for the higher temperature experiment showed a change in shape of the mechanical response and distinct changes in transformation front patterns over 31 partial transformation cycles.

An Experimental Setup for Measuring Unstable Thermo-Mechanical Behavior of Shape Memory Alloy Wire

An experimental arrangement is demonstrated that overcomes some difficulties in thermo-mechanical testing of thin Shape Memory Alloy (SMA) wires under uniaxial tension. It is now well known that stress-induced transformations in some SMAs under uniaxial loading can lead to mechanical instabilities and propagating phase transformation fronts. Critical parameters, such as nucleation barriers are difficult to measure by conventional testing techniques and are often masked by unavoidable stress concentrations at grips. In addition, simultaneous full field measurements of localized deformation and temperature fields are difficult to obtain for different ambient conditions. The current scheme uses a temperature-controlled conduction block and a non-uniform temperature field induced by thermoelectric modules to uncover the underlying thermo-mechanical response of the wire. The approach also allows access for optical and infrared imaging of the specimen deformation and temperature fields.

Buckling of steel bars with Lüders bands

Abstract Experiments and simulations are presented for the study of interaction between material and structural instabilities that occur in mild steel bars under axial compression. The material instability consists of Luders bands that nucleate and propagate along the specimens. The structural instability involves lateral deflections of the bar leading to collapse. The study includes an investigation of bars of several different lengths. The mechanical response in the experiments were monitored through measurements of axial load, axial and midspan lateral displacements, and full field imaging of a brittle coating showing the Luders deformation. Interesting interactions exist between the localized deformation due to the material-level instabilities and the global collapse of the bars. Finite element simulations, using a constitutive model with a nonmonotonic stress–strain behavior, showed good agreement with the experiments and helped to explain the variety of collapse modes seen in the experiments. The symmetry of imperfections and/or loading misalignments have dramatic effects on the evolution of Luders deformation and the eventual collapse mode. Certain imperfections lead to deformation modes that delay structural collapse.

A model for calculating diffraction elastic constants

A model, dubbed the inverse Kroner model, is proposed to calculate the diffraction elastic constants from the elastic constants of a single crystal. It is related to the classic Kroner model, and both are identified as bounds on the diffraction elastic constants. Through the grain shape as controlling parameter, the classic Kroner model is bound by the hkl-independent mechanical limit given by the bulk elastic constants of the matrix, while the inverse Kroner model approaches the Reuss limit.

5754 Aluminum Sheet Deformed Along Bi‐Linear Strain Paths

Sheet specimens of aluminum alloy 5754 were deformed along a series of bi‐linear, equal‐biaxial and uniaxial, strain paths while simultaneously measuring stress‐strain behavior. Using the measured crystallographic texture before and after deformation, the VPSC model that incorporates texture evolution was used to simulate the flow stress and hardening behavior. Including latent hardening of multiple slip planes allowed the model to explain the decrease in flow stress when changing from equal‐biaxial to uniaxial deformation. However, the model did not capture the details of the drop in flow stress nor the magnitude of the plastic hardening after the change in deformation mode. This is likely due to room temperature recovery between the two steps of testing.

Thermodynamics of a 1D shape memory alloy: modeling, experiments, and application

A thermomechanical model for a shape memory alloy (SMA) wire under uniaxial loading is implemented in a finite element framework, and its results are compared with new experimental data. The constitutive model is a one-dimensional continuum model of an SMA element, including two internal field variables, strain gradient effects, possible unstable mechanical behavior, and the relevant thermomechanical couplings resulting from latent heat effects. The model is calibrated to recent experiments of typical commercially available polycrystalline NiTi wire. The shape memory effect and pseudoelastic behaviors are demonstrated numerically as a function of applied loading rate and environmental parameters, and the results are found to be quite similar to experimental data. The model is then used to simulate a simple SMA actuator device, and the model proves to be a useful tool to assess the performance.

Advanced Biaxial Cruciform Testing at the NIST Center for Automotive Lightweighting

Modeling of sheet metal forming operations requires mechanical properties data at very large tensile strains and various biaxial strain paths. Typically these data are developed along strain ratio paths that are linear and monotonic, but actual forming strain paths are nonlinear and not necessarily monotonically increasing. A unique planar-biaxial testing facility at the National Institute of Standards and Technology (NIST) has been designed to address non-linear strain paths and other long standing measurement needs. The system uses a combination of four independently controlled hydraulic actuators, with either displacement, force, or strain feedback control, to deform the material, while measurements of the material response is accomplished through a unique combination of digital image correlation and X-ray diffraction. Results of commissioning tests are presented for displacement and force control along different axes. The system was able to deform the sample in the elastic and plastic regimes. The results show the difference between the displacement and strain paths followed, as well as some unexpected behavior (e.g. buckling). Other expanded system capabilities for future use are briefly described.

Constitutive Relations for AA 5754 Based on Crystal Plasticity

Constitutive equations for the multiaxial stress-strain behavior of aluminum alloy 5754 sheets were developed, based on crystal plasticity. A Taylor-based polycrystal plasticity model, a tangent formulation of the self-consistent viscoplastic model (VPSC), and an N-site viscoplastic model based on the fast Fourier transform (VPFFT) were used to fit a single slip system hardening law to the available data for tension, plane strain, and biaxial stretching. The fitting procedure yields good agreement with the monotonic stress-strain data, with similar parameter values for each model. When simulating multiaxial tests using the developed hardening law, models that allow both stress and strain variations in grains give better predictions of the stress-strain curves. Furthermore, generally, the simulated texture evolution is too rapid when compared to the experiments. By incorporating a more detailed neighbor interaction effect, the VPFFT model predicts texture evolution in better agreement with experiments.

Validation of Uniaxial Data Beyond Uniform Elongation

Uniaxial testing is one of the simplest methods used to determining mechanical properties for sheet metals, but the classic test does not determine properties to sufficiently high strain levels for use in models of very large deformations such as forming operations. This limitation is primarily due to the classical test requiring uniform deformation in the gage length. Full-field optical techniques are now being used to extend the applicable strain range of uniaxial testing to strains beyond uniform elongation and well into diffuse necking, but assumptions must be made as to the multi-axial state of stress in this regime. In order to determine if such assumptions are correct, uniaxial experiments are performed combined with a unique combination of digital image correlation to measure plastic strains and stress tensor measurement through X-ray diffraction methods. The combination of metrology permits determination of the true stress-strain response to strains four times uniform elongation and the associated multi-axial stresses at the highest strain levels.