Multiaxial and non-proportional loading responses,anisotropy and modeling of Ti–6Al–4V titanium alloy over wide ranges of strain rates and temperatures

Results from a series of multiaxial loading experiments on the Ti–6Al–4V titanium alloy are presented. Different loading conditions are applied in order to get the comprehensive response of the alloy. The strain rates are varied from the quasi-static to dynamic regimes and the corresponding material responses are obtained. The specimen is deformed to large strains in order to study the material behavior under finite deformation at various strain rates. Torsional Kolsky bar is used to achieve shear strain rates up to 1000 s⁻¹. Experiments are performed under non-proportional loading conditions as well as dynamic torsion followed by dynamic compression at various temperatures. The non-proportional loading experiments comprise of an initial uniaxial loading to a certain level of strain followed by biaxial loading, using a channel-type die at various rates of loadings. All the non-proportional experiments are carried out at room temperature. Experiments are also performed to investigate the anisotropic behavior of the alloy. An orthotropic yield criterion [proposed by Cazacu, O., Plunkett, B., Barlat, F., 2005. Orthotropic yield criterion for hexagonal closed packed metals. International Journal of Plasticity 22, 1171–1194.] for anisotropic hexagonal closed packed materials with strength differential is used to generate the yield surface. Based on the definition of the effective stress of this yield criterion, the observed material response for the different loading conditions under large deformation is modeled using the Khan–Huang–Liang (KHL) equation assuming isotropic hardening. The model constants used in the present study, were pre-determined from the extensive uniaxial experiments presented in the earlier paper [Khan, A.S., Suh, Y.S., Kazmi R., 2004. Quasi-static and dynamic loading responses and constitutive modeling of titanium alloys. International Journal of Plasticity 20, 2233–2248]. The model predictions are found to be extremely close to the observed material response.     

Experimental investigation and modeling of the tension behavior of polycarbonate with temperature effects from low to high strain rates

The effects of strain rate and temperature on the tension stress–strain responses of polycarbonate are experimentally investigated over a wide range of strain rates (0.001–1700 s⁻¹) and temperatures (0–120 °C). A modified split Hopkinson tension bar is used for high-rate uniaxial tension tests. Experimental results indicate that the stress–strain responses of polycarbonate at high strain rates exhibit the nonlinear characteristics including the obvious yielding and strain softening. The tension behavior is strongly dependent on the strain rate and temperature. The values of yield stress and strain at yield present a dramatic increase at higher strain rates and decrease with the increase in temperature. Moreover, there exists a significant rate-sensitivity transition in the polycarbonate tension yield behavior. Based on the experimental investigation, a physically based three-dimensional elastoplastic constitutive model for the finite deformation of glassy polymers is used to characterize the rate-temperature dependent yield and post-yield behavior of polycarbonate when subjected to tension loading. The model results are shown close to the experimental data within the investigated strain-rate and temperature ranges.     

Micromechanics, macromechanics and constitutive modeling of the elasto-viscoplastic deformation of rubber-toughened glassy polymers

Under certain conditions, such as sufficiently low temperatures, high loading rates and/or highly triaxial stress states, glassy polymers display an unfavorable characteristic—brittleness. A technique used for reducing the brittleness (increasing the fracture toughness) of these materials is rubber toughening. While there is significant qualitative understanding of the mechanical behavior of rubber-toughened polymers, quantitative modeling tools for the large-strain deformation of rubber-toughened glassy polymers are largely lacking.In this paper, we develop a suite of numerical tools to investigate the mechanical behavior of rubber-toughened glassy polymers, with emphasis on rubber-toughened polycarbonate. The rubber particles are modeled as voids in view of their deformation-induced cavitation early during deformation. A three-dimensional micromechanical model of the heterogeneous microstructure is developed to study the effects of initial rubber particle (void) volume fraction on the underlying elasto-viscoplastic deformation mechanisms in the material, and how these mechanisms influence the macroscopic response of the material. A continuum-level constitutive model is developed for the large-strain elasto-viscoplastic deformation of porous glassy polymers, and it is calibrated against micromechanical modeling results for porous polycarbonate. The constitutive model can be used to study various boundary value problems involving rubber-toughened (porous) glassy polymers. As an example, the case of an axisymmetric notched bar is simulated for the case of polycarbonate with varying levels of initial porosity. The quality of the constitutive model calibration is assessed using a multi-scale modeling approach.     

Anisotropic responses, constitutive modeling and the effects of strain-rate and temperature on the formability of an aluminum alloy

Finite deformation anisotropic responses of AA5182-O, over a wide range of strain-rates (10⁻⁴ to 10⁰ s⁻¹) and temperatures (293-473 K) are presented. The plastic anisotropy parameters were experimentally determined from tensile experiments using specimens from sheet material. Using the experimental results under plane stress conditions, the anisotropy coefficients for Barlat’s yield function (YLD96) were calculated at different strain-rates and temperatures. The correlations obtained from YLD96 are in good agreement with the observed experimental results. The strain-rate sensitivity of AA5182-O alloy changed from negative at 293 K to positive at 473 K. Khan-Huang-Liang (KHL) constitutive model is shown to correlate the observed strain-rate and temperature dependent responses reasonably well. The material parameters were obtained from the experimental responses along the rolling direction (RD) of the sheet. Marciniak and Kuckzinsky (M-K) theory was used to obtain the theoretical strain and stress-based forming limit curves (FLCs) at different strain-rates and temperatures. The experimental result from the published literature is compared with the FLCs from the current study.     

Three-dimensional modeling and numerical analysis of rate-dependent irrecoverable deformation in shape memory alloys

Shape memory alloys (SMAs) provide an attractive solid-state actuation alternative to engineers in various fields due to their ability to exhibit recoverable deformations while under substantial loads. Many constitutive models describing this repeatable phenomenon have been proposed, where some models also capture the effects of rate-independent irrecoverable deformations (i.e., plasticity) in SMAs. In this work, we consider a topic not addressed to date: the generation and evolution of irrecoverable viscoplastic strains in an SMA material. Such strains appear in metals subjected to sufficiently high temperatures. The need to account for these effects in SMAs arises when considering one of two situations: the exposure of a conventional SMA material (e.g., NiTi) to high temperatures for a non-negligible amount of time, as occurs during shape-setting, or the utilization of new high temperature shape memory alloys (HTSMAs), where the elevated transformation temperatures induce transformation and viscoplastic behaviors simultaneously. A new three-dimensional constitutive model based on established SMA and viscoplastic modeling techniques is derived that accounts for these behaviors. The numerical implementation of the model is described in detail. Several finite element analysis (FEA) examples are provided, demonstrating the utility of the new model and its implementation in assessing the effects of viscoplastic behaviors in shape memory alloys.     

Dynamic compressive responses of intact and damaged ceramics from a single split Hopkinson pressure bar experiment

A novel dynamic compressive experimental technique has been developed based on a split Hopkinson pressure bar. This new method dynamically loads the ceramic specimen by two consecutive stress pulses. The first pulse determines the dynamic response of the intact ceramic materiaal and then crushes the specimen, and the second pulse determines the dynamic compressive constitutive behavior of the ceramic rubble. Precise pulse shaping ensures that the specimen deforms at nearly constant strain rates under dynamic stress equilibrium during the loading by both stress pulses. Pulse shaping also controls the amplitudes of loading pulses, the values of strain rates, the maximum strains in the rubble specimens, and the proper separation time between the two loading pulses. The feasibility of the new technique is demonstrated by the experimental results obtained on an AD995 alumina.     

Effect of oxygen content and microstructure on the thermo-mechanical response of three Ti–6Al–4V alloys: Experiments and modeling over a wide range of strain-rates and temperatures

Results from a series of experiments on three different titanium alloys, under quasi-static and dynamic loading conditions are presented. The Ti–6Al–4V titanium alloys include the ELI version and two with higher oxygen contents. The strain-rates are varied from 10⁻⁶ to 3378 s⁻¹ while observations are made at temperatures from 233 to 755 K. The alloys initial and deformed photomicrographs and various deformation mechanisms responsible for the induced plastic deformation, are presented and discussed. Differences in the responses of these alloys are observed in terms of thermal softening, work hardening, and strain-rate and temperature sensitivities. The Khan–Huang–Liang (KHL) model is used to effectively simulate the observed responses obtained from these experiments. The model, with the constants determined from these experiments, is then used to predict strain-rate jump experimental results, and also high temperature dynamic experiments for one of the alloys; the predictions are found to be very close to the observations.