A convergence analysis of the affine particle-in-cell method and its application in the simulation of extrusion processes

Simulation of extrusion processes represents a large challenge for commonly used numerical methods. In our application for example, a hot melt is extruded whilst being rapidly cooled. Under these conditions of quenching, spinodal phase separation occurs which causes the formation of a characteristic micro-structure of the extrudate, consisting of solid and liquid phases. We model this process using a variant of the Material Point Method (MPM) [4], namely the Affine Particle-In-Cell (APIC) method [13]. Its hybrid particle/grid character is advantageous for simulating both fluid and solid behavior: pure Eulerian particle methods, such as classic SPH, fail for simulating solids, particularly in tension, whereas pure Lagrangian methods generally cannot cope with large deformations caused by material flow. APIC improves upon the original MPM method by using a so-called locally affine velocity representation [13] which allows the conservation of linear and angular momentum without the need of potentially unstable Fluid-Implicit-Particle (FLIP) techniques [3]. We analyze the convergence behavior of APIC and compare its accuracy against a traditional MPM variant, the Generalized Interpolation Material Point Method (GIMP)

Simulation of vapour-liquid condensation in dipolar fluids and uniform sampling Monte Carlo algorithms

This works examines the question whether a vapour-liquid phase transition exists in systems of particles with purely dipolar interactions, a topic which has been the subject of a longstanding debate. Monte Carlo simulation results for two modi operandi to tackle this issue are presented. One approach examines the phase behaviour of fluids of charged hard dumbbells (CHD), each made up of two oppositely charged hard spheres with diameters σ and separation d. In the limit d/σ → 0, and with the temperature scaled accordingly, the system corresponds to dipolar hard spheres (DHS) while for larger values of d ionic interactions are dominant. The crossover between ionic and dipolar regimes is examined and a linear variation of the critical temperature T*c in dipolar reduced units as a function of d is observed, giving rise to an extrapolated T*cDHS ≈ 0:15. The second approach focuses on the dipolar Yukawa hard sphere (DYHS)fluid, which is given by a dipolar hard sphere and an attractive isotropic interaction Y of the Yukawa tail form. In this case, the DHS limit is obtained for Y → 0. It is found that T*c depends linearly on the isotropic interaction strength Y over a wide range, coinciding with the results for the CHD model and extrapolating to a similar value of T*c;DHS. However, with the use of specially adapted biased Monte Carlo techniques which are highly efficient, it is shown that the linear variation of T*c is violated for very small values of the Yukawa interaction strength, almost two orders of magnitude smaller than the characteristic dipolar interaction energy. It is found that phase separation is not observable beyond a critical value of the Yukawa energy parameter, even though in thermodynamic and structural terms, the DYHS and DHS systems are very similar. It is suggested that either some very subtle physics distinguishes the DYHS and DHS systems, or the observation of a phase transition in DHSs is precluded by finite-size effects. In the context of phase separation in highly correlated fluids, new flat-histogram Monte Carlo simulation techniques based on the Wang-Landau algorithm are evaluated and shown to be useful tools. This work presents a general and unifying framework for deriving Monte Carlo acceptance rules which facilitate flat histogram sampling. The framework yields uniform sampling rules for thermodynamic states given either by the mechanically extensive variables appearing in the Hamiltonian or, equivalently, uniformly sample the thermodynamic fields which are conjugate to these mechanical variables

Strain measurement by contour analysis

Background: The determination of yield stress curves for ductile metals from uniaxial material tests is complicated by the presence of tri-axial stress states due to necking. A need exists for a straightforward solution to this problem. Objective: This work presents a simple solution for this problem specific to axis-symmetric specimens. Equivalent uniaxial true strain and true stress, corrected for triaxiality effects, are calculated without resorting to inverse analysis methods. Methods: A computer program is presented which takes shadow images from tensile tests, obtained in a backlight configuration. A single camera is sufficient as no stereoscopic effects need to be addressed. The specimen's contours are digitally extracted, and strain is calculated from the contour change. At the same time, stress triaxiality is computed using a novel curvature fitting algorithm. Results: The method is accurate as comparison with manufactured solutions obtained from Finite Element simulations show. Application to 303 stainless steel specimens at different levels of stress triaxiality show that equivalent uniaxial true stress -- true strain relations are accurately recovered. Conclusions: The here presented computer program solves a long-standing challenge in a straightforward manner. It is expected to be a useful tool for experimental strain analysis

The effect of compression shock heating in collision welding

This work discusses the origin of temperature rise during the collision welding process. The different physical irreversible and reversible mechanisms which act as heat sources are described: isentropic compression work, shock dissipation, plasticity, and phase transitions. The temperature increase due to these effects is quantified in a continuum mechanics approach, and compared to predictions of atomistic molecular dynamics simulations. Focusing on a single impact scenario of 1100 aluminium at 700 m/s, our results indicate that shock heating and plastic work only effect a temperature rise of 100 K, and that the effects of phase change are not significant. This temperature rise cannot explain welding. In consequence, the relevant mechanism which effects bonding in collision welding must be due to the jet, which is only formed at oblique impact angles

Programming Strain Rate Dependency into Mechanical Metamaterials

This work presents an approach to introduce significant strain rate sensitivity into metallic metamaterials that are manufactured via additive manufacturing, where the base material employed will typically have a weak strain rate sensitivity. Here, we employ friction between the rough surfaces as the strain-rate dependent mechanism, whose magnitude is tunable by optimizing the geometry. The design along with the preliminary simulation results of the friction unit cell is presented. This work will quantify the effects of geometrical parameters on the dissipated energy

A constant acoustic impedance mount for sheet-type specimens in the tensile Split-Hopkinson Bar

This paper addresses a problem well-known amongst practitioners of the Split-Hopkinson Tension Bar method: attaching a flat test specimen made from sheet material to the cylindrical input-and output bars. To date, slotting the bar ends and gluing the specimens into these ends with high-strength adhesives is the gold standard. However, this approach is not universally applicable because some materials are difficult to bond, and the adhesion surface is limited by the bar diameter, meaning that only small width specimens can be tested. In contrast, the hitherto published mechanical clamping mechanisms typically introduce excessive additional mass into the Split-Hopkinson system which detrimentally affects wave propagation and thus causes errors in the stress-strain signals. We circumvent this problem by designing a mechanical clamping device which has the same acoustic impedance as the bar material and is suitable to securely attach specimens with a width larger than the bar diameter. The benefits of our new clamping device are demonstrated by reporting tensile stress-strain data for Polycarbonate at high strain rates. The data is free from unwanted oscillations and enables accurate determination of dynamic strength and stiffness