A Finite Element to Perform 3D Shakedown Analysis for Limited Kinematic Hardening Materials

The use of the Design by Analysis (DBA) route is a modern trend in pressure vessel and piping international codes in mechanical engineering. However, to apply the DBA to structures under variable mechanical and thermal loads, it is necessary to assure that the plastic collapse modes, alternate plasticity and incremental collapse (with instantaneous plastic collapse as a particular case), be precluded. The tool available to achieve this target is the shakedown theory. Unfortunately, the practical numerical applications of the shakedown theory result in very large nonlinear optimization problems with nonlinear constraints. Precise, robust and efficient algorithms and finite elements to solve this problem in finite dimension has been a more recent achievements. However, to solve real problems in an industrial level, it is necessary also to consider more realistic material properties as well as to accomplish 3D analysis. Limited kinematic hardening, is a typical property of the usual steels and it should be considered in realistic applications. In this paper, a new finite element with internal thermodynamical variables to model kinematic hardening materials is developed and tested. This element is a mixed ten nodes tetrahedron and through an appropriate change of variables is possible to embed it in a shakedown analysis software developed by Zouain and co-workers for elastic ideally-plastic materials, and then use it to perform 3D shakedown analysis in cases with limited kinematic hardening materials

Shakedown Analysis Considering Limited Kinematic Hardening Materials

In design or safety assessment of mechanical structures, the use of the Design by Analysis (DBA) route is a modern trend. However, for making possible to apply DBA to structures under variable loads, two basic failure modes considered by ASME or European Standards must be precluded. Those modes are the alternate plasticity and incremental collapse (with instantaneous plastic collapse as a particular case). Shakedown theory is a tool that permit us to assure that those kinds of failures will be avoided. However, in practical applications, very large nonlinear optimization problems are generated. Due to this facts, only in recent years have been possible to obtain algorithms sufficiently accurate, robust and efficient, for dealing with this class of problems. In this paper, one of these shakedown algorithms, developed for dealing with elastic ideally-plastic structures, is enhanced to include limited kinematic hardening, a more realistic material behavior. This is done in the continuous model by using internal thermodynamic variables. A corresponding discrete model is obtained using an axisymmetric mixed finite element with an internal variable. A thick wall sphere, under variable thermal and pressure loads, is used in an example to show the importance of considering the limited kinematic hardening in the shakedown calculations

A critical reassessment of elastic unloading in sharp instrumented indentation experiments and the extraction of mechanical properties

This work examines the extraction of mechanical properties from instrumented indentation P-h(s) curves via extensive three-dimensional finite element analyses for pyramidal tips in a wide range of solids under frictional and frictionless contact conditions. Since the topography of the imprint changes with the level of pile-up or sink-in, a relationship is identified between correction factor beta in the elastic equation for the unloading indentation stage and the amount of surface deformation effects. It is shown that the presumption of a constant beta significantly affects mechanical property extractions. Consequently, a new best-fit function is found for the correlation between penetration depth ratios h(e)/h(max), h(r)/h(max) and n, circumventing the need for the assumption of a constant value for beta, made in our prior investigation [Acta Mater. 53 (2005) pp. 3545-3561]. Simulations under frictional contact conditions provide sensible boundaries for the influence of friction on both h(e)/h(max) and h(r)/h(max). Friction is essentially found to induce an overestimation in the inferred n. Instrumented indentation experiments are also performed in three archetypal metallic materials exhibiting distinctly different contact responses. Mechanical property extractions are finally demonstrated in each of these materials.

Finite element and dimensional analysis algorithm for the prediction of mechanical properties of bulk materials and thin films

In this work, the applicability of a new algorithm for the estimation of mechanical properties from instrumented indentation data was studied for thin films. The applicability was analyzed with the aid of both three-dimensional finite element simulations and experimental indentation tests. The numerical approach allowed studying the effect of the substrate on the estimation of mechanical properties of the film, which was conducted based on the ratio h(max)/l between maximum indentation depth and film thickness. For the experimental analysis, indentation tests were conducted on AISI H13 tool steel specimens, plasma nitrated and coated with TiN thin films. Results have indicated that, for the conditions analyzed in this work, the elastic deformation of the substrate limited the extraction of mechanical properties of the film/substrate system. This limitation occurred even at low h(max)/l ratios and especially for the estimation of the values of yield strength and strain hardening exponent. At indentation depths lower than 4% of the film thickness, the proposed algorithm estimated the mechanical properties of the film with accuracy. Particularly for hardness, precise values were estimated at h(max)/l lower than 0.1, i.e. 10% of film thickness. (C) 2010 Published by Elsevier B.V.

Precipitation hardening of Cu-Fe-Cr alloys - Part I - Mechanical and electrical properties

This research is part of a project whose scope was to investigate the engineering properties of new non-commercial alloy formulations based on the Cu rich corner of the Cu-Fe-Cr ternary system with the primary aim of exploring the development of a new cost-effective high-strength, high-conductivity copper alloy. The literature indicated that Cu rich Cu-Cr and Cu-Fe alloys have been thoroughly investigated. A number of commercial alloys have been developed and these are used for a variety of applications requiring combinations of high-strength, high-conductivity and resistance to softening. Little evidence was found in the literature that the Cu rich corner of the Cu-Fe-Cr system had previously been investigated for the purpose of developing high-strength, high-conductivity copper alloys resistant to softening. The aim of these present investigations was to explore the possibility that new alloys could be developed that combined the properties of both sets of alloys, ie large precipitation hardening response combined with the ability to stabilise cold worked microstructures to high temperatures while at the same maintain high electrical conductivity. To assess the feasibility of this goal the following alloys were chosen for investigation: Cu-0.7wt%Cr-0.3wt%Fe, Cu-0.7wt%Cr-0.8wt%Fe, Cu-0.7wt%Cr-2.0wt%Fe. This paper reports on the mechanical property investigation which indicated that the Cu-0.7wt%Cr-0.3wt%Fe, and Cu-0.7wt%Cr-2.0wt%Fe alloys were worthy of further investigation. (C) 2001 Kluwer Academic Publishers.

Precipitation hardening of Cu-Fe-Cr alloys - Part II - Microstructural characterisation

This research is part of a project whose scope was to investigate the engineering properties of new non-commercial alloy formulations based on the Cu rich corner of the Cu-Fe-Cr ternary system with the primary aim of exploring the development of a new cost-effective high-strength, high-conductivity copper alloy. Promising properties have been measured for the following alloys: Cu-0.7wt%Cr-0.3wt%Fe and Cu-0.7wt%Cr-2.0wt%Fe. This paper reports on the microstructural characterisation of these alloys and discusses the mechanical and electrical properties of these alloys in terms of their microstructure, particularly the formation of precipitates. These alloys have evinced properties that warrant further investigation. Cost modelling has shown that Cu-0.7wt%Cr-0.3wt%Fe is approximately 25% cheaper to produce than commercial Cu-1%Cr. It has also been shown to be more cost efficient on a yield stress and % IACS per dollar basis. The reason for the cost saving is that the Cu-0.7%Cr-0.3%Fe alloy can be made with low carbon ferro-chrome additions as the source of chromium rather than the more expensive Cu-Cr master-alloy. For applications in which cost is one of the primary materials selection criteria, it is envisaged that there would be numerous applications in both cast and wrought form, where the Cu-0.7%Cr-0.3%Fe alloy would be more suitable than Cu-1%Cr. (C) 2001 Kluwer Academic Publishers.

An age hardening model for Al-7Si-Mg casting alloys

Yield strength (YS) ageing curves have been modelled for A356 and A357 aluminium casting alloys below the solvus temperature of the main hardening precipitate. Predictions are based on the Shercliff and Ashby methodology (Acta MetaH. Mater. 38 (1990) 1789) for wrought alloys. Differences between strengthening in wrought and cast Al-Si-Mg alloys are considered. A Brinell hardness to YS conversion incorporating strain hardening has been established to enable YS ageing curves to be predicted with reduced experimental effort. (C) 2002 Elsevier Science B.V. All rights reserved.

Lime-metakaolin mortars for historical buildings repair: study of the hardening reaction

International Conference Durable Structures: from construction to rehabilitation. Lisbon, LNEC, 31 May-1 June 2012

Plastic-damage smeared crack model to simulate the behaviour of structures made by cement based materials

This work proposes a constitutive model to simulate nonlinear behaviour of cement based materials subjected to different loading paths. The model incorporates a multidirectional fixed smeared crack approach to simulate crack initiation and propagation, whereas the inelastic behaviour of material between cracks is treated by a numerical strategy that combines plasticity and damage theories. For capturing more realistically the shear stress transfer between the crack surfaces, a softening diagram is assumed for modelling the crack shear stress versus crack shear strain. The plastic damage model is based on the yield function, flow rule and evolution law for hardening variable, and includes an explicit isotropic damage law to simulate the stiffness degradation and the softening behaviour of cement based materials in compression. This model was implemented into the FEMIX computer program, and experimental tests at material scale were simulated to appraise the predictive performance of this constitutive model. The applicability of the model for simulating the behaviour of reinforced concrete shear wall panels submitted to biaxial loading conditions, and RC beams failing in shear is investigated.

Magnetic hardening mechanisms in Nd-Fe-B nanocrystalline material

Microstructural and magnetic measurements of the evolution by heat treatment of initially amorphous Nd16Fe76B8 alloys prepared by melt spinning are presented. Evidence of magnetic hardening above a threshold temperature induced by magnetic isolation of the Nd2Fe14B grains is provided. A thermodynamic and kinetic explanation of local melting of the intergranular nanostructured Nd¿rich eutectic phase at temperatures below 900 K based on capillary effects is presented. A subsequent Ostwald ripening process moves Nd to wet intimately the hard magnetic grains, becoming, on cooling, a real paramagnetic isolating thin film (~2.5 nm). By using a simple analogy, it is shown that the switching magnetization field in a single¿domain crystal can be drastically affected through the exchange coupling to neighboring grains with different orientation of the easy axis. This effect should be important enough to reinforce the coercive field of polycrystalline hard magnetic materials and explains the observed enhancement from 0.9 to 1.9 T.

Electronic origin of bond softening and hardening in femtosecond-laser-excited magnesium

Many ultrafast structural phenomena in solids at high fluences are related to the hardening or softening of particular lattice vibrations at lower fluences. In this paper we relate femtosecond-laser-induced phonon frequency changes to changes in the electronic density of states, which need to be evaluated only in the electronic ground state, following phonon displacement patterns. We illustrate this relationship for a particular lattice vibration of magnesium, for which we—surprisingly—find that there is both softening and hardening as a function of the femtosecond-laser fluence. Using our theory, we explain these behaviours as arising from Van Hove singularities: We show that at low excitation densities Van Hove singularities near the Fermi level dominate the change of the phonon frequency while at higher excitations Van Hove singularities that are further away in energy also become important. We expect that our theory can as well shed light on the effects of laser excitation of other materials.

Hardening of concrete with a planned delayed ettringite formation

Delayed ettringite formation (DEF) in cementitious materials is widely considered as a harmful chemical reaction that causes extensive damages in hardened concrete. However, preventative measures and possible improvements in general are not extensively studied and require further attention. In this study was presented an investigation into a type of controlled DEF in places of finely dispersed crystallisation nuclei and provide evidence that the process may improve compressive strength of cementitious materials. The Alkali-Silica Reaction (ASR) in hydrated concrete was achieved with the addition of fly ash and was further accelerated with the Duggan’s test. Achieved strengths and monitoring of microstructure development conducted with electronic microscopy revealed that growth of ettringite crystals in the nuclei led to harmless internal compressive stresses, expansion of hydrated concrete and overall strengthening of the concrete matrix.

Homogenization of Precipitation Hardening Nickel Based Superalloys

Allvac 718 Plus and Haynes 282 are relatively new precipitation hardening nickel based superalloys with good high temperature mechanical properties. In addition, the weldability of these superalloys enhances easy fabrication. The combination of high temperature capabilities and superior weldability is unmatched by other precipitation hardening superalloys and linked to the amount of the γ’ hardening precipitates in the materials. Hence, it is these properties that make Allvac 718 Plus and Haynes 282 desirable in the manufacture of hot sections of aero engine components. Studies show that cast products are less weldable than wrought products. Segregation of elements in the cast results in inhomogeneous composition which consequently diminishes weldability. Segregation during solidification of the cast products results in dendritic microstructure with the segregating elements occupying interdendritic regions. These segregating elements are trapped in secondary phases present alongside γ matrix. Studies show that in Allvac 718Plus, the segregating phase is Laves while in Haynes 282 the segregating phase is not yet fully determined. Thus, the present study investigated the effects of homogenization heat treatments in eliminating segregation in cast Allvac 718 Plus and Haynes 282. Paramount to the study was the effect of different homogenization temperatures and dwell time in the removal of the segregating phases. Experimental methods used to both qualify and quantify the segregating phases included SEM, EDX analysis, manual point count and macro Vickers hardness tests. Main results show that there is a reduction in the segregating phases in both materials as homogenization proceeds hence a disappearance of the dendritic structure. In Allvac 718 Plus, plate like structures is observed to be closely associated with the Laves phase at low temperatures and dwell times. In addition, Nb is found to be segregating in the interdendritic areas. The expected trend of increase in Laves as a result of the dissolution of the plate like structures at the initial stage of homogenization is only detectable for few cases. In Haynes 282, white and grey phases are clearly distinguished and Mo is observed to be segregating in interdendritic areas.

Effects of substituting ytterbium for scandium on the microstructure and age-hardening behaviour of Al-Sc alloy

In order to reduce the cost of Al-Sc alloys and maintain their mechanical properties, the microstructure and mechanical properties of Al-0.24 wt% Sc-0.07 wt% Yb in comparison with Al-0.28 wt% Sc alloys were studied. The aging behaviour, precipitate morphologies, precipitate coarsening and precipitation hardening of both alloys were investigated. The average diameter and the size distribution of nanoscale Al3Sc and Al-3(Sc,Yb) precipitates at various aging conditions were measured. Transmission electron microscopy (TEM) and high-resolution TEM were used to deeply understand the precipitate evolution. A maximum hardness around 73 (HV30) was obtained with a precipitate diameter from 4.3 to 5.6 nm for both alloys. (c) 2014 Elsevier B.V. All rights reserved.

Further results in J and CTOD estimation procedures for SE(T) fracture specimens - Part I: Homogeneous materials

This study provides further developments of the evaluation procedure for J and CTOD in SE(T) fracture specimens based on plastic eta-factors and load separation analysis. Non-linear finite element analyses for plane-strain and 3-D models provide the relationship between plastic work and crack driving forces which define the eta-values. Further analyses based on the load separation method define alternative eta-values for the analyzed specimen configurations. Overall, the present results provide improved estimation equations for J and CTOD as a function of loading condition (pin load vs. clamp ends), crack geometry and strain hardening properties. (C) 2011 Elsevier Ltd. All rights reserved.