Developing Microstructure- And Dislocation-Based Constitutive Numerical Models For Predicting The Mechanical Behaviour Of Dmls Ti6Al4V(Eli) At Various Strain Rates

Abstract

Direct metal laser sintering (DMLS) is among the new technologies being pursued by many academic research centres, materials scientists and engineers in the aerospace and biomedical industries as a potential replacement of conventional manufacturing technologies. A scrupulous understanding of the DMLS processes and related post- processes is crucial for establishment of this technology as the better alternative manufacturing route for Ti6Al4V(Extra Low Interstitial-ELI), an alloy commonly used in these industries. The success of such processes depends on the achievement of good structural mechanical properties of Ti6Al4V(ELI), comparable or even superior to those of the conventionally produced alloy. The macroscopic properties of materials are largely affected by the microstructure. The microstructure is a very intricate feature with various aspects that influence specific properties in both a synergistic and competing manner. The morphologies and size of grains, crystallographic texture, macro process-residual stresses and defects, which are largely dislocations in nature, are among these aspects. To accelerate the acceptance of DMLS Ti6Al4V(ELI) in industry, numerical models that can quantitatively describe the interrelationships between the microstructural features, field variables, such as temperature and strain rate, and the mechanical properties are necessary. At the initial stage of the present study, an analytical constitutive model that is sensitive to the microstructure of Ti6Al4V was developed. Various microstructures of DMLS Ti6Al4V(ELI) were produced via heat treatment and characterised to determine critical microstructural parameters of the model. Experimental tests at selected strain rates and temperatures were then undertaken for these microstructures of DMLS Ti6Al4V(ELI) to acquire data for use in determining the critical parameters of this model. The arising refined and validated analytical constitutive model was then implemented as material user subroutine in ABAQUS/Explicit to generate numerical solutions. Simulation tests were then carried out to determine the predictive capacity of the developed model. Various mechanisms that prevail during yielding and plastic flow in Ti6Al4V were examined. Using these mechanisms, an advanced analytical model was developed to provide a macroscopic description of the flow properties of various microstructures of DMLS Ti6Al4V(ELI) for a wide range of field variables. The critical microstructural features of average α-grain size and initial dislocation density that influence the plastic deformation were explicitly articulated in the formulation of this model. The effects of the heat treatment processes on the morphologies, size and crystallographic texture of the microstructural grains were first investigated. The microstructures of the non-heat-treated and heat-treated samples of DMLS Ti6Al4V(ELI) were examined using an optical microscope (OM) and a scanning electron microscope (SEM). A SEM equipped with a backscattered electron detector for electron backscatter diffraction (EBSD) analysis was used for crystallographic texture analysis. The β-phase texture from this data was ascertained based on a reconstruction method using the Automatic Reconstruction of Parent Grain for EBSD data (ARPGE) program. The average α՛/α grain-size was observed to increase from a value of < 1.5 μm for the non-heat-treated samples to a value of about 9 μm for the samples that were heat-treated above the α→β grain transformation temperature. The intensity of texture was also seen to increase because of heat treatment, with the maximum unit density (MUD) of the α՛/α-phase in the basal plane (0001) increasing from 4.9 in the non-heat-treated samples to 24 for samples that were heat-treated at the highest temperature. The non-heat-treated samples and those samples that were heat-treated to just below the α→β-grain transformation temperature showed a strong fibrous texture of the reconstructed β-grains with the 〈100〉 directions almost parallel to the build direction. The alignment of the fibrous texture in the build direction disappeared after heat treatment above the α→β-grain transformation temperature. An analysis of the X-ray diffraction (XRD) profiles of the non-heat-treated and heat-treated microstructures of DMLS Ti6Al4V(ELI) was carried out to determine the level of defects in these microstructures. The modified Williamson-Hall and modified Warren- Averbach methods of analysis were used to evaluate the dislocation densities in these microstructures. The results obtained showed a 73% reduction of dislocation density in DMLS Ti6Al4V(ELI) upon stress-relieving heat treatment at a temperature of 650°C for a period of 3 hours. The density of dislocations further declined in microstructures that were annealed at elevated temperatures, with the microstructures that were heat-treated just below the α→β-grain transformation temperature recording the lowest dislocation densities. The high cooling rate gradient normally associated with the DMLS process leads to formation of a non-equilibrium martensitic microstructure. Our previous study demonstrated that this microstructure possesses inferior dynamic deformation properties compared to the microstructure arising from use of conventional manufacturing processes. Thus, in the present study the compressive high-strain-rate properties and deformation behaviour of DMLS Ti6Al4V(ELI) were studied for samples that were heat-treated above the martensitic transformation temperature. High-strain- rate compression tests were carried out using a Split Hopkinson Pressure Bar (SHPB) test system at temperatures of 25 °C, 200 °C and 500 °C. The tests at each temperature were conducted at three different average plastic strain rates of 750 s-1, 1500 s-1 and 2450 s-1 and flow stress curves at these test conditions were obtained. Comparative analyses of these flow stress curves for different categories of samples were then carried out. The flow stress curves of all samples tested generally showed the flow stress to increase with increasing strain rate and to decrease with increasing temperature. These observations showed that the microstructures of Ti6Al4V(ELI) are sensitive to both strain rate and temperature. The samples that were heat-treated at lower temperatures showed the highest dynamic yield stress at any temperature and strain rate compared to those that were heat-treated at elevated temperatures. An examination and analysis of the deformed surfaces of tested samples using SEM showed these surfaces to be dominated by adiabatic shear bands (ASBs) that were predominantly inclined at an angle of ≈45° to the loading axis. This suggested that the compressive fracturing of these samples at high strain rate was because of the development of ASBs. The flow stress curves of different samples were then used to obtain and refine the calibration parameters of the analytical constitutive model that are sensitive to the microstructure of the samples developed here. In these equations, the strain hardening and dynamic recovery that are normally experienced by materials during high-strain-rate deformation were articulated by two model calibration parameters ℎ and 𝑘2, respectively. The influence of initial dislocation densities on the flow properties of Ti6Al4V(ELI) according to the models developed here was investigated. It was shown that for high initial dislocation densities, the shape of the stress-strain curve was that of a pronounced peak stress followed by a decreasing flow stress. Lower initial dislocation densities led to a decreased peak stress and, in some cases, this decrease was followed by a state where no strain hardening occurred. The expected decrease of flow stress with increasing temperature was demonstrated well by the model developed here. The upturn of flow stress at high strain rate was taken care of by the introduction of a viscous drag stress component that is sensitive to high strain rates. This stress component for different samples was calibrated with experimental data using two fitting parameters. The microstructure-based constitutive numerical model developed and validated here using experimental data showed good capacity to predict the high- strain-rate flow properties of additively manufactured Ti6Al4V(ELI) alloy. This was demonstrated by the statistical performance measures of the correlation coefficients (𝑅2) and the absolute average error (δ). The values of 𝑅2 and δ obtained for correlation of the model and experimental values of various samples were >0.976 and <6% , respectively. This high correlation is an indication of the robustness of the model developed here in predicting the high-strain-rate properties of DMLS Ti6Al4V(ELI). The validated microstructure- and dislocation-based analytical constitutive model was then implemented as a user material subroutine in ABAQUS using VUMAT and VUHARD subroutines. This was followed by verification. Initially, the verification process was conducted for single and multiple element tests with varying prescribed loading conditions. The simulation results obtained were then compared with the analytical solutions which showed a good capacity of both the developed VUMAT and VUHARD subroutines to be used for high-strain-rate simulations. The verification process was then extended further for tests devised to study the dynamic properties of materials at high strain rates, in this case the SHPB test. Comparison between the SHPB simulation of numerical and experimental results showed excellent correlation, with the correlation coefficient and average absolute error being > 0.97 and < 4%, respectively for various samples. This showed that the numerical model is suitable for use in designing the dynamic strength of DMLS Ti6Al4V(ELI) structures for high strain rate applications, by controlling the morphology of its microstructure and the initial dislocation density present in the alloy.