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.     

Modeling the dynamic response of visco-elastic open-cell foams

This article introduces a mesoscopic formulation for modeling the dynamic response of visco-elastic, open-cell solid foams. The effective material response is obtained by enforcing on a representative 3D unit cell the principle of minimum action for dissipative systems. The resulting model accounts explicitly for the foam topology, the elastic and viscous properties of the cell wall, and the inertial effects arising from non-affine motion within the cells. The microinertial effects become significant in retarding the foam collapse during exceedingly high strain-rate loading. As an application example, a heterogenous case of compressive deformation at high strain rate is simulated utilizing the present model as a constitutive update in a non-linear finite element analysis code. This FEM simulation shows the ability of the model to capture the progressive foam collapse during the dynamic compression as observed in experimental studies. Using the microscopic model, the inertial and viscous strain-rate effects are investigated through the foam density, viscosity, and relative density. Based on the physics incorporated into the local cell model, we provide insight into the physical mechanisms responsible for the experimentally observed strain-rate effects on the behavior of dynamically loaded foam materials.     

Simulation of damage evolution in ductile metals undergoing dynamic loading conditions

A set of constitutive equations for large rate-dependent elastic-plastic-damage materials at elevated temperatures is presented to be able to analyze adiabatic high strain rate deformation processes for a wide range of stress triaxialities. The model is based on the concepts of continuum damage mechanics. Since the material macroscopic thermo-mechanical response under large strain and high strain rate deformation loading is governed by different physical mechanisms, a multi-dissipative approach is proposed. It incorporates thermo-mechanical coupling effects as well as internal dissipative mechanisms through rate-dependent constitutive relations with a set of internal variables. In addition, the effect of stress triaxiality on the onset and evolution of plastic flow, damage and failure is discussed.Furthermore, the algorithm for numerical integration of the coupled constitutive rate equations is presented. It relies on operator split methodology resulting in an inelastic predictor-elastic corrector technique. The explicit finite element program LS-DYNA augmented by an user-defined material subroutine is used to approximate boundary-value problems under dynamic loading conditions. Numerical simulations of dynamic experiments with different specimens are performed and good correlation of numerical results and published experimental data is achieved. Based on numerical studies modified specimens geometries are proposed to be able to detect complex damage and failure mechanisms in Hopkinson-Bar experiments.     

Strain rate dependency of uniaxial tensile strength in Gosford sandstone by the Distinct Lattice Spring Model with X-ray micro CT

Mechanisms causing strain rate dependency of the uniaxial tensile strength of Gosford sandstone are studied using the Distinct Lattice Spring Model (DLSM). The DLSM is built to have a microstructure which resembles aspects of the microstructure in a sample of the sandstone observed through 5 μm resolution X-ray micro CT scanning. Numerical dynamic uniaxial tensile tests on the sandstone are performed using both X-ray micro CT based and homogenous particle models. The results indicate that there is an only negligible strength increase with increasing strain rate for the homogenous particle model. However, a significant strength increase is observed with increasing strain rate for the X-ray micro CT based particle model. Therefore, it must be the microstructure that causes a strain rate dependency. Moreover, the influence of viscosity and rate dependency of springs are also studied. Results reveal that the rate dependency of the springs rather than their viscosity is also a main cause of the rate dependency.