Micromechanics-based multiscale modelling for damage prediction in forging biocompatible alloys

Abstract

The prediction of damage initiation and evolution is always a key concern in metal forming processes. There are two main approaches used for damage prediction in metallic materials, i.e., the continuum damage mechanics (CDM)-based model and the micromechanics-based damage (micro-damage) model. The former of these uses continuum thermodynamics and continuum mechanics to study the effects of damage on the mechanical response induced by irreversible processes; while the latter adopts a constitutive model to evaluate the effects of void nucleation, growth and coalescence inside the material. The micro-damage model is used widely nowadays due to the sound physical understanding of damage caused fundamentally by micro-void evolution in metallic material. In the application of the micro-damage model for damage prediction, the identification of micro-void initiation and growth is of great importance. Destructive methods that focus on the measurement of specific two-dimensional (2D) sections are tedious and incomplete. Non-destructive X-ray computed tomography (CT) is believed to be an ideal alternative technique as it allows for all-round visualization and quantification of the internal micro-voids in three dimensions. However, the application of the X-ray CT technique for damage parameter identification in the micro-damage model has received little research attention. In addition, most of the constitutive models coupled with damage have been formulated within the small deformation framework, which limits their applications in the large deformation processes of metallic materials with good plasticity. This research work, thus, aimed to develop a micromechanics-based multiscale framework for damage prediction in the large deformation of metallic materials undergoing forging. Typical biocompatible alloys, i.e., stainless steel 316L (SS316L) and titanium alloy Ti-6Al-4V, were used as specimen materials to carry out the X-ray CT scanning, uniaxial tensile and compression tests, as well as forging experiments. A micro-focus high-resolution X-ray CT system was employed to detect and measure the micro-voids of the specimen directly and precisely. A multiscale homogenization approach, based on the concept of representative volume element (RVE), was employed to transform the microscopic RVE' behaviours to macroscopic material properties. Then the developed multiscale damage model was implemented into FE packages (e.g., ABAQUS) for damage prediction. Finally, the damage evolutions at both cold forging and warm forging were predicted and verified experimentally. The main contributions of this research work are summarized as follows: (1) The damage constitutive model under small deformation conditions was extended to a large deformation framework based on the logarithmic objective rate. By introducing an independent variable f, i.e., the volume fraction of micro-voids, into the damage constitutive laws, a micro-damage model concerned with the evolution of micro-voids was developed for damage prediction in the large deformation of metallic materials. A multiscale homogenization approach, based on the concept of RVE, was employed to transform the microscopic RVE' behaviours to macroscopic material properties. The specific constitutive equations were compiled and implemented into ABAQUS as a user-defined subroutine for damage prediction. (2) Various geometrical RVE models were constructed based on the assumption to analyse the influence of micro-void configurations (i.e., volume fractions, shapes and spatial locations) on the stress-strain behaviour of the material under tensile and compressive deformations at a microscopic scale. Furthermore, the actual micro-voids inside the SS316L specimens were detected by the X-ray CT system. The sizes, volume fractions and distributions of the micro-voids were analysed and compared between two different process conditions (i.e., cast and cold-rolled). (3) The nature of ductile damage, i.e., the nucleation, growth and coalescence of micro-voids were studied systematically, with the aid of X-ray CT and loading-unloading experiments. The damage evolution laws of SS316L at both tension and compression with a wide range of stress states were revealed. These experimental findings not only provide accurate material damage parameters for the development of multiscale micro-damage model, but also can be used for the verification of damage prediction. (4) A specific forging tooling system was designed for warm-forging a medical implant, i.e., the basal thumb implant. X-ray CT scanning was carried out for both the preformed and forged components. 3D volumetric CT images were then reconstructed and the 3D micro-void distribution and evolution inside the materials were detected and analysed quantitatively. Furthermore, typical local strain regions were established as 3D RVE models for both SS316L and Ti-6Al-4V preforms. The spatial location, size and volume of each micro-void were obtained from defect analysis of the 3D CT images and considered for subsequent damage prediction of the RVE models. An improved thermo-mechanical coupled micro-damage model, with the interaction between deformation and heat transfer taken into consideration, was established based on the thermodynamic relations and logarithmic stress rate. The localized damage evolutions at both compressive and tensile deformations were predicted and found to match quite well with the experimental findings.