Discrete dislocation dynamics analysis of the effect of lattice orientation on void growth in single crystals

The micromechanisms of plastic deformation and void growth were analyzed using discrete dislocation dynamics in an isolated FCC single crystal deformed in-plane strain in the plane. Three different stress states (uniaxial tension, uniaxial deformation and biaxial deformation) were considered for crystals oriented in different directions and with a different number of active slip systems. It was found that strain hardening and void growth rates depended on lattice orientation in uniaxial tension because of anisotropic stress state. Crystal orientation did not influence, however, hardening and void growth when the crystals were loaded under uniaxial or biaxial deformation because the stress state was more homogeneous, although both (hardening and void growth rates) were much higher than under uniaxial tension. In addition, the number of active slip systems did not substantially modify the mechanical behavior and the void growth rate if plastic deformation along the available slip systems was compatible with overall crystal deformation prescribed by the boundary conditions. Otherwise, the incompatibility between plastic deformation and boundary conditions led to the development of large hydrostatic elastic stresses, which increased the strain hardening rate and reduced the void growth rate

Simulation of the deformation of polycrystalline nanostructured Ti by computational homogenization

Computational homogenization by means of the finite element analysis of a representative volume element of the microstructure is used to simulate the deformation of nanostructured Ti. The behavior of each grain is taken into account using a single crystal elasto-viscoplastic model which includes the microscopic mechanisms of plastic deformation by slip along basal, prismatic and pyramidal systems. Two different representations of the polycrystal were used. Each grain was modeled with one cubic finite element in the first one while many cubic elements were used to represent each grain in the second one, leading to a model which includes the effect of grain shape and size in a limited number of grains due to the computational cost. Both representations were used to simulate the tensile deformation of nanostructured Ti processed by ECAP-C as well as the drawing process of nanostructured Ti billets. It was found that the first representation based in one finite element per grain led to a stiffer response in tension and was not able to predict the texture evolution during drawing because the strain gradient within each grain could not be captured. On the contrary, the second representation of the polycrystal microstructure with many finite elements per grain was able to predict accurately the deformation of nanostructured Ti

A roadmap for virtual testing and virtual processing of cast metallic materials

A multiscale modeling strategy is presented to carry out virtual design, virtual processing and virtual testing of metallic alloys for engineering applications manufactured by casting. Multiscale modeling will be tackled using a bottom-up, hierarchical approach. Modeling efforts begin with ab initio simulations and bridging of the length and time scales will be accomplished through different multiscale strategies which will encompass the whole range of length and time scales required by virtual design, virtual processing and virtual testing. Nevertheless, not everything can or should be computed and critical experiments are an integral part of the program for the calibration and validation of the multiscale strategies. Examples of application of the different parts of the strategy to simulate the microstructure and the properties of Ni-based superalloy components manufactured by investment casting for the aerospace industry will be presented

Dislocation Dynamics in Non-conves Domains using Finite Elements with Embedded Discontinuities

The standard strategy developed by Van der Giessen and Needleman (1995 Modelling Simul. Mater. Sci. Eng. 3 689) to simulate dislocation dynamics in two-dimensional finite domains was modified to account for the effect of dislocations leaving the crystal through a free surface in the case of arbitrary non-convex domains. The new approach incorporates the displacement jumps across the slip segments of the dislocations that have exited the crystal within the finite element analysis carried out to compute the image stresses on the dislocations due to the finite boundaries. This is done in a simple computationally efficient way by embedding the discontinuities in the finite element solution, a strategy often used in the numerical simulation of crack propagation in solids. Two academic examples are presented to validate and demonstrate the extended model and its implementation within a finite element program is detailed in the appendix

Finite Deformation of Porous Elastomers: A Computational Micromechanics Approach

Finite Deformation of Porous Elastomers: A Computational Micromechanics Approac

Latent hardening size effect in small-scale plasticity

We aim at understanding the multislip behaviour of metals subject to irreversible deformations at small-scales. By focusing on the simple shear of a constrained single-crystal strip, we show that discrete Dislocation Dynamics (DD) simulations predict a strong latent hardening size effect, with smaller being stronger in the range [1.5 µm, 6 µm] for the strip height. We attempt to represent the DD pseudo-experimental results by developing a flow theory of Strain Gradient Crystal Plasticity (SGCP), involving both energetic and dissipative higher-order terms and, as a main novelty, a strain gradient extension of the conventional latent hardening. In order to discuss the capability of the SGCP theory proposed, we implement it into a Finite Element (FE) code and set its material parameters on the basis of the DD results. The SGCP FE code is specifically developed for the boundary value problem under study so that we can implement a fully implicit (Backward Euler) consistent algorithm. Special emphasis is placed on the discussion of the role of the material length scales involved in the SGCP model, from both the mechanical and numerical points of view

A level set approach for the analysis of flow and compaction during resin infusion in composite materials

Fluid flow and fabric compaction during vacuum assisted resin infusion (VARI) of composite materials was simulated using a level set-based approach. Fluid infusion through the fiber preform was modeled using Darcy’s equations for the fluid flow through a porous media. The stress partition between the fluid and the fiber bed was included by means of Terzaghi’s effective stress theory. Tracking the fluid front during infusion was introduced by means of the level set method. The resulting partial differential equations for the fluid infusion and the evolution of flow front were discretized and solved approximately using the finite differences method with a uniform grid discretization of the spatial domain. The model results were validated against uniaxial VARI experiments through an [0]8 E-glass plain woven preform. The physical parameters of the model were also independently measured. The model results (in terms of the fabric thickness, pressure and fluid front evolution during filling) were in good agreement with the numerical simulations, showing the potential of the level set method to simulate resin infusio

Comportamiento en Fractura de un fieltro de fibra de vidrio

The deformation and damage micromechanisms of a glass-fiber non-woven felt were analyzed with a combination of experiments and simulations. Tensile tests were performed on unnotched and notched rectangular specimens to study the physical nature of damage. It was found that fracture was controlled by interbundle bond fracture followed by frictional sliding, leading to the localization of damage in a wide band. A random network model based on finite elements was developed in order to gain a better understanding of the experimental data. The simulations were in very good agreement with the data and contributed to explain features such as the effect of specimen dimensions on the strength of the material and its notch-insensitive behavior

Modelización numérica del comportamiento mecánico de un fieltro de polipropileno

En el presente trabajo se presenta un modelo del continuo para un fieltro denso. Igualando la densidad de potencia de un elemento del continuo a la densidad de potencia mecánica que actúa sobre el conjunto de las fibras se obtiene una expresión del tensor de tensiones en la configuración de referencia. El modelo se completa mediante la inclusión de un modelo de daño para modelar fenomenológicamente los mecanismos de extracción (pull-out) y rotura de las fibras. Se ha implementado el modelo como una subrutina de material de usuario para un código de elementos finitos (ABAQUSExplicit), formulado en grandes deformaciones. Los resultados obtenidos se han comparado con experimentos realizados sobre un fieltro comercial (geotextil) de fibras de polipropileno y muestran que el modelo es capaz de reproducir el comportamiento del material hasta la localización del daño y pérdida de capacidad portante del mismo

An inverse optimization strategy to determine single crystal mechanical behavior from polycrystal tests: Application to AZ31 Mg alloy

An inverse optimization strategy was developed to determine the single crystal properties from experimental results of the mechanical behavior of polycrystals. The polycrystal behavior was obtained by means of the finite element simulation of a representative volume element of the microstructure in which the dominant slip and twinning systems were included in the constitutive equation of each grain. The inverse problem was solved by means of the Levenberg-Marquardt method, which provided an excellent fit to the experimental results. The iterative optimization process followed a hierarchical scheme in which simple representative volume elements were initially used, followed by more realistic ones to reach the final optimum solution, leading to important reductions in computer time. The new strategy was applied to identify the initial and saturation critical resolved shear stresses and the hardening modulus of the active slip systems and extension twinning in a textured AZ31 Mg alloy. The results were in general agreement with the data in the literature but also showed some differences. They were partially explained because of the higher accuracy of the new optimization strategy but it was also shown that the number of independent experimental stress-strain curves used as input is critical to reach an accurate solution to the inverse optimization problem. It was concluded that at least three independent stress-strain curves are necessary to determine the single crystal behavior from polycrystal tests in the case of highly textured Mg alloys