A granular model of solidification as applied to hot tearing

Hot cracking is a spontaneous failure of an alloy during solidification. It is a severe problem for casting industry as it reduces the productivity of cast houses and limits the range of alloys compositions that can be industrially produced. Hot tears occurs at the end of solidification, when solid grains are separated by thin liquid films. At this stage of solidification, fluid flow between the grains is difficult and the solid network is not continuous enough to transmit stresses. The material is extremely brittle. Moreover, the deformation induced by the thermal shrinkage of the material tends to localize in hot spots, i.e., in zones which solidify at last. These zones become in tension and the concomitant effect of the tensile stress with the intrinsic brittleness of the material result in a hot crack. Even though the general mechanisms of hot tearing are understood, the importance of each physical parameter remains ill defined. The present work is mainly focused on the derivation of a granular model of mushy zone (the zone where solid and liquid coexist) for aluminium alloys, i.e., a model which explicitly considers the behaviour of each grain while being sufficiently simple to allow the computation of large mushy zones. First, a solidification model based on the Voronoi diagram of a random set of nuclei is derived. This model computes the solidification in each polyhedron considering back-diffusion and coalescence. Second, a pressure drop calculation is performed in the network of connected liquid channels assuming the centre of solid grains to be fixed. This model considers a Poiseuille flow in each channel, Kirchhoff's conservation of flow at nodal points and flow Losses compensating solidification (KPL model). Finally, the displacement of the solid grain centres is considered and the mechanical behaviour of the mushy zone is computed assuming perfectly rigid solid grains. This model shows the progressive formation of grain clusters and the localization of fluid flow at high solid fraction. Therefore, it allows to define transitions in the behaviour of the mushy zone. These transitions are essential for hot cracking models, but should be introduced as parameters in continuum approaches. Finally, the mechanical model shows a strong localization of deformation in liquid channels normal to the stress direction. Such channels create ideal sites for the nucleation and the propagation of hot cracks.

Two-phase modelling of hot tearing in aluminium alloys using a semi-coupled method

Vincent Mathier

Hot tearing is one of the most severe defects observed in castings, e.g. in billets or sheet ingots of aluminum alloys produced by DC casting. It is due to both tensile strains and a lack of interdendritic feeding in the mushy zone. In order to predict this phenomenon at the scale of an entire casting, the two-phase averaged conservation equations for mass and momentum must be solved in the mushy (i.e. mixed solid and liquid) region of the material. In recent contributions, M'Hamdi et al [1] proposed a strongly coupled resolution scheme for this set of equations. The solution of the problem was obtained using a rheological model established by Ludwig et al [2] and that captures the partially cohesive nature of the mushy alloy. In the present contribution, the problem is addressed using a slightly different approach. The same rheological model (i.e. saturated porous media treatment) is used, but the influence of the liquid pressure is neglected at this stage. This assumption allows for a weakly coupled resolution scheme in which the mechanical problem is first solved alone using ABAQUS™ and user subroutines. Then the pressure in the liquid phase is calculated separately accounting for the viscoplastic deformation of the porous solid skeleton and solidification shrinkage. This is done with a code previously developed for porosity calculations, and that uses a refined mesh in the mushy zone [3]. This semi-coupled method was implemented and its numerical convergence studied from the point of view of both time step and mesh size. Guidelines for selecting these numerical parameters as well as the conditions under which the semi-coupled method may be applied are provided. The model was then applied to three cases, i.e. two tensile tests conducted on mushy alloys [4, 5] and the casting of an entire billet [6]. Experimental data was indeed available concerning these problems prior to the present work. This information was used for the validation of the thermal and mechanical models that were setup to describe these different cases. The results of the semi-coupled approach were also used to describe in more details these different castings. First of all, the numerical study of the mushy zone tearing test [5] proved helpful for distinguishing different fracture modes. The role of the high strain rate applied to the mushy alloy in this case was also outlined. Another tensile test, referred to as the rig test [4], was successfully modeled in the present framework. The numerical results could be used to quantify the redistribution of strain in the mushy sample. As a consequence, intrinsic properties of the material, such as its ductility, could be extracted from the results. This study also gave further insight about the conditions under which tearing occurs in the samples. Finally, the semi-coupled method was used to study the DC casting process. In this case, a real process performed under realistic conditions for the production of an industrial scale billet was modeled. As it is more complex and difficult to characterize experimentally, the conditions for hot tearing formation are less accessible. However, the isotherm velocity, the strain, the strain rate and the liquid pressure could be described reasonably accurately. It was thus possible to correlate experimental observations of the hot tear with various calculated indicators of hot tearing susceptibility. Even with this information, it remains difficult to formulate new hot tearing criteria because all the indicators follow a similar trend during the casting and their respective contributions can thus not be distinguished. The present work showed that the level of accuracy and detail that can be reached using two-phase models with appropriate materials properties and boundary conditions is satisfactory. It is indeed possible to model the relevant phenomena (heat flow, solid deformation and liquid feeding) at the scale of an entire casting. The variation of the different simulated fields can be described down to a scale of the order of a few millimeters. In that sense, this approach is one important aspect required to build a multiscale model for the problem of hot tearing. It is expected that coupling such a method with granular models (which cover length scales from a few microns to a few centimeters [7]) will allow for a more complete description of the phenomena at hand. In the future, the development of such a multiscale numerical tool may prove to be the most efficient way towards quantitative predictions of hot tearing formation in real solidification processes.

EPFL2007

Time-Dependent Response of Ultra High Performance Fibre Reinforced Concrete (UHPFRC) under Low to High Tensile Stresses

Agnieszka Ewa Switek

Ultra High Performance Fibre Reinforced Concretes (UHPFRC) are characterised by high mechanical performance, extremely low permeability and tensile strain hardening. For structural applications, in composite structures they are very well adapted for reinforcement and protection of existing concrete members. Cast in-situ, they undergo under restraint development of tensile eigenstresses at early age, which can lead in some specific cases of applications to localised macrocracking of a new layer and loss of protective function. On the other hand their tensile viscoelastic potential helps mitigate these stresses. The objective of this study was to investigate the tensile viscoelastic properties of UHPFRC at early ages and long-term in creep and relaxation tests. A large experimental campaign with tensile creep and relaxation tests was performed, with load levels ranging from 30 to 90% of the tensile strength, including creep and relaxation tests during the strain hardening phase, at two different loading ages of 3 and 7 days. Three main testing setups were used: TSTM (Temperature Stress Testing Machine), creep rigs and closed-loop servo-hydraulic testing machine with additional Acoustic Emission detection. The influence of early age evolution in mechanical response and underlying mechanisms governing this response were discussed. Linear viscoelastic models were used to analyse and to highlight on the basis of the experimental results the non-linear behavior depending on solicitation level and loading sequence. The non-linear threshold for viscoelastic response was estimated for the material loaded at 3 and 7 days. The early age mechanical response at 3 days was proportional to the load level in the instantaneous part for three stress levels tested 30, 60 and 90% of the tensile strength, and showed non-linear creep from 60% on. It was observed that for a very low stress level of 13% the creep deformation was decreasing. Relaxation tests with compensation of simultaneously monitored shrinkage deformation were performed, and showed a viscoelastic potential similar to the one observed for creep for the low load level of 30%. Incremental creep and relaxation tests were successfully performed for 3 days age specimens. For higher stress levels, the viscoelastic response from creep tests was more pronounced than in relaxation tests, which was highlighted by analysis with linear viscoelastic models. The creep response at 7 days showed that the threshold for non-linear viscoelasticity is close to 9 MPa (81% of the tensile strength) load level. The Acoustic Emission non-destructive testing method was used to get insight on the physical mechanisms involved in viscoelastic deformations. A strong correlation between AE number of events and the deformation was found, also the amplitude and energy of AE events was found to be of the same order during the instantaneous and delayed deformations. UHPFRC loaded at 7 days age in incremental test showed linear behavior until very high stress level corresponding to the hardening domain. The non-linear and tertiary creep was obtained during the last loading step, for 12 and 11 MPa respectively, which occurred in the hardening domain. The Acoustic Emission monitoring confirmed very close correlation between non-linear creep and AE cumulative number of events induced by microcracking. In order to precisely detect non-linear phenomena in incremental test, analysis with linear viscoelastic models was performed. Comparison between creep and relaxation test results showed that non-linear viscoelastic phenomena were more actively involved in creep tests. The outcomes of this research, bridging the material science and structural engineering, provide useful data to foster applications in new and existing structures, making the best use of the tensile viscoelastic potential of UHPFRC.

EPFL2011

Three-dimensional granular model of semi-solid metallic alloys undergoing solidification: Fluid flow and localization of feeding

Jean-Marie Drezet, André Phillion, Michel Rappaz, Meisam Sistaninia

A three-dimensional (3-D) granular model which simulates fluid flow within solidifying alloys with a globular microstructure, such as that found in grain refined Al alloys, is presented. The model geometry within a representative volume element (RVE) consists of a set of prismatic triangular elements representing the intergranular liquid channels. The pressure field within the liquid channels is calculated using a finite elements (FEs) method assuming a Poiseuille flow within each channel and flow conservation at triple lines. The fluid flow is induced by solidification shrinkage and openings at grain boundaries due to deformation of the coherent solid. The granular model predictions are validated against bulk data calculated with averaging techniques. The results show that a fluid flow simulation of globular semi-solid materials is able to reproduce both a map of the 3-D intergranular pressure and the localization of feeding within the mushy zone. A new hot cracking sensitivity coefficient is then proposed. Based on a mass balance performed over a solidifying isothermal volume element, this coefficient accounts for tensile deformation of the semi-solid domain and for the induced intergranular liquid feeding. The fluid flow model is then used to calculate the pressure drop in the mushy zone during the direct chill casting of aluminum alloy billets. The predicted pressure demonstrates that deep in the mushy zone where the permeability is low the local pressure can be significantly lower than the pressure predicted by averaging techniques. (C) 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.