Three-dimensional molecular dynamics simulations of void coalescence during dynamic fracture of ductile metals

Void coalescence and interaction in dynamic fracture of ductile metals have been investigated using three-dimensional strain-controlled multi-million atom molecular dynamics simulations of copper. The correlated growth of two voids during the coalescence process leading to fracture is investigated, both in terms of its onset and the ensuing dynamical interactions. Void interactions are quantified through the rate of reduction of the distance between the voids, through the correlated directional growth of the voids, and through correlated shape evolution of the voids. The critical inter-void ligament distance marking the onset of coalescence is shown to be approximately one void radius based on the quantification measurements used, independent of the initial separation distance between the voids and the strain-rate of the expansion of the system. The interaction of the voids is not reflected in the volumetric asymptotic growth rate of the voids, as demonstrated here. Finally, the practice of using a single void and periodic boundary conditions to study coalescence is examined critically and shown to produce results markedly different than the coalescence of a pair of isolated voids.Comment: Accepted for publication in Physical Review

A General Solution to the Aircraft Trim Problem

Trim defines conditions for both design and analysis based on aircraft models. In fact, we often define these analysis points more broadly than the conditions normally associated with trim conditions to facilitate that analysis or design. In simulations, these analysis points establish initial conditions comparable to flight conditions. Based on aerodynamic and propulsion systems models of an aircraft, trim analysis can be used to provide the data needed to define the operating envelope or the performance characteristics. Linear models are typically derived at trim points. Control systems are designed and evaluated at points defined by trim conditions. And these trim conditions provide us a starting point for comparing one model against another, one implementation of a model against another implementation of the same model, and the model to flight-derived data. In this paper we define what we mean by trim, examine a variety of trim conditions that have proved useful and derive the equations defining those trim conditions. Finally we present a general approach to trim through constrained minimization of a cost function based on the nonlinear, six-degree-of freedom state equations coupled with the aerodynamic and propulsion system models. We provide an example of how a trim algorithm is used with a simulation by showing an example from JSBSim

Multiscale characterisation of the mechanical properties of austenitic stainless steel joints

A multiscale investigation was pursued in order to obtain the strain distribution and evolution during tensile testing both at the macro- and micro-scale for a diffusion bonded 316L stainless steel. The samples were designed for the purpose to demonstrate that the bond line properties were equal or better than the parent material in a sample geometry that was extracted from a larger component. The macroscopic stress-strain curves were coupled to the strain distributions using a camera-based 2D – Digital Image Correlation system. Results showed significant amount of plastic deformation predominantly concentrated in shear bands which were extended over a large region, crossing through the joint area. Yet it was not possible to be certain whether the joint has shown significant plastic deformation. In order to obtain the joints’ mechanical response in more detail, in situ micromechanical testing was conducted in the SEM chamber that allowed areas of 1x1 mm2 and 50x50 mm2 to be investigated. The size of the welded region was rather small to be accurately captured from the camera based DIC system. Therefore a microscale investigation was pursued where the samples were tested within an SEM chamber. Low magnification SEM imaging was utilised in order to cover a viewing area of 1 mm×1 mm while high magnification SEM imaging was employed to provide evidence of the occurrence of plastic deformation within the joint, at an area of just 50 μm×50 μm. The strain evolution over the microstructural level, within the joint and at the base material was obtained. The local strains were highly non-homogeneous through the whole test. Final failure occurred approximately 0.2 mm away from the joint. Large local strains were measured within the joint region, while SEM imaging showed that plastic deformation occurs via the formation of strong slip bands, followed by the activation of additional slip systems upon further plastic deformation which end up in additional slip bands to form on the surface. Plastic deformation occurred by slip and twinning mechanisms. Upon necking, significant out of plane deformations and slip deformation mechanisms were observed which suggested that plastic deformation was also happening at the last stages of damage evolution for the specific alloy. This was also evident from the large difference between the 600 MPa UTS stress value and the low stress values before final failure (which in many cases was below 30 MPa)

Effect of stress-triaxiality on void growth in dynamic fracture of metals: a molecular dynamics study

The effect of stress-triaxiality on growth of a void in a three dimensional single-crystal face-centered-cubic (FCC) lattice has been studied. Molecular dynamics (MD) simulations using an embedded-atom (EAM) potential for copper have been performed at room temperature and using strain controlling with high strain rates ranging from 10^7/sec to 10^10/sec. Strain-rates of these magnitudes can be studied experimentally, e.g. using shock waves induced by laser ablation. Void growth has been simulated in three different conditions, namely uniaxial, biaxial, and triaxial expansion. The response of the system in the three cases have been compared in terms of the void growth rate, the detailed void shape evolution, and the stress-strain behavior including the development of plastic strain. Also macroscopic observables as plastic work and porosity have been computed from the atomistic level. The stress thresholds for void growth are found to be comparable with spall strength values determined by dynamic fracture experiments. The conventional macroscopic assumption that the mean plastic strain results from the growth of the void is validated. The evolution of the system in the uniaxial case is found to exhibit four different regimes: elastic expansion; plastic yielding, when the mean stress is nearly constant, but the stress-triaxiality increases rapidly together with exponential growth of the void; saturation of the stress-triaxiality; and finally the failure.Comment: 35 figures, which are small (and blurry) due to the space limitations; submitted (with original figures) to Physical Review B. Final versio

Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models

A unified variational theory is proposed for a general class of multiscale models based on the concept of Representative Volume Element. The entire theory lies on three fundamental principles: (1) kinematical admissibility, whereby the macro- and micro-scale kinematics are defined and linked in a physically meaningful way; (2) duality, through which the natures of the force- and stress-like quantities are uniquely identified as the duals (power-conjugates) of the adopted kinematical variables; and (3) the Principle of Multiscale Virtual Power, a generalization of the well-known Hill-Mandel Principle of Macrohomogeneity, from which equilibrium equations and homogenization relations for the force- and stress-like quantities are unequivocally obtained by straightforward variational arguments. The proposed theory provides a clear, logically-structured framework within which existing formulations can be rationally justified and new, more general multiscale models can be rigorously derived in well-defined steps. Its generality allows the treatment of problems involving phenomena as diverse as dynamics, higher order strain effects, material failure with kinematical discontinuities, fluid mechanics and coupled multi-physics. This is illustrated in a number of examples where a range of models is systematically derived by following the same steps. Due to the variational basis of the theory, the format in which derived models are presented is naturally well suited for discretization by finite element-based or related methods of numerical approximation. Numerical examples illustrate the use of resulting models, including a non-conventional failure-oriented model with discontinuous kinematics, in practical computations

Investigation of the effect of forming parameters in incremental sheet forming using a micromechanics based damage model

The incremental sheet forming (ISF) process is considered as a feasible solution for forming a variety of small batch and even customised sheet components. The quality of an ISF product is affected by various process parameters, e.g. sheet material, step-down, feed rate, tool diameter and lubricant. To produce an ISF part of sufficient quality and accuracy without defects, optimal parameters of the ISF process should be selected. In the present work, experiments and FE analyses were conducted to evaluate the influence of the main ISF process parameters including the step-down, feed rate and tool diameter on the formability and fracture of two types of pure Ti (grade 1 and 2). The Gurson–Tvergaard-Needleman (GTN) damage constitutive model with consideration of stress triaxiality was developed to predict ductile fracture in the ISF process due to void nucleation, growth and coalescence. It was found that the ISF parameters have varying degrees of effect on the formability and fracture occurrence of the two types of pure Ti, and grade 2 pure Ti sheet is more sensitive than grade 1 Ti sheet to the forming parameters due to low ductility