Comparison of mechanical behaviour of thin film simulated by discrete dislocation dynamics and continuum crystal plasticity

3D finite element simulations of 9-grain multicrystalline aggregates are performed within the framework of the classical continuum crystal plasticity and discrete dislocation dynamics. The results are processed in a statistical way by ensemble averaging. The comparison is made at three levels: macroscopic stress–strain curves, average stress values per grain, local values of stress and plastic strain. The comparison shows that some similarities are observed in the stress and strain distributions in both simulations approaches. But there are also large discrepancies caused by the discrete nature of plasticity in DDD. The DDD simulations provide higher stress levels in the aggregate due to the small number of dislocation sources and to the stress field induced by individual dislocations.

Sensitivity of deformation twinning to grain size in titanium and magnesium

The impact of grain size on deformation twinning in commercial purity titanium and magnesium alloy Mg–3Al–1Zn (AZ31) is investigated. Tensile tests were carried out for the titanium samples; compression testing was employed for the magnesium specimens. Average values of the true twin length, true twin thickness and the number density of twins were determined using stereology. A key difference between these two materials is that twinning contributes little to the plastic strain in the titanium while it accounts for nearly all of the early plastic strain in the magnesium. In some respects (e.g. volume fraction and number density) the phenomenology of twinning differed between the two materials, while in others (e.g. twin shape and size) both materials showed a similar response. It is found that in both materials, twins span the entirety of their parent grains only for grain sizes less than ∼30 μm. Both the nucleation density per unit of nucleating interface (i.e. grain and twin boundaries) and the aspect ratio of twins scale with applied stress. The impact of grain size on twin volume fraction is modelled analytically.

Springback investigation in roll forming of a V-section

To have fuel efficient vehicles with a lightweight structure, the use of High Strength Steels (HSS) and Advanced High Strength Steels (AHSS) in the body of automobiles is increasing. Roll forming is used widely to form AHSS materials. Roll forming is a continuous process in which a flat strip is shaped to the desired profile by passing through numerous sets of rolls. Formability and springback are two major concerns in the roll forming of AHSS materials. Previous studies have shown that the elastic modulus (Young's modulus) of AHSS materials can change when the material undergoes plastic deformation and the main goal of this study is to numerically investigate the effect of a change in elastic modulus during forming on springback in roll forming. Experimental loading-unloading tests have been performed to obtain the material properties of TRIP 700 steel and incorporate those in the material model used in the numerical simulation of the roll forming process. The finite element simulations were carried out using MSC-Marc and two different element types, a shell element and a solid-shell element, were investigated. The results show that the elastic modulus diminution due to plastic strain increases the springback angle by about 60% in the simple V-section roll forming analyzed in this study. © (2014) Trans Tech Publications, Switzerland.

Improved contact load-bearing capacity of ultra-fine grained titanium : Multilayering and grading

The contact load-bearing response and surface damage resistance of multilayered hierarchical structured (MHSed) titanium were determined and compared to monolithic nanostructured titanium. The MHS structure was formed by combining cryorolling with a subsequent Surface Mechanical Attrition Treatment (SMAT) producing a surface structure consisted of an outer amorphous layer containing nanocrystals, an inner nanostructured layer and finally an ultra-fine grained core. The combination of a hard outer layer, a gradual transition layer and a compliant core results in reduced indentation depth, but a deeper and more diffuse sub-surface plastic deformation zone, compared to the monolithic nanostructured Ti. The redistribution of surface loading between the successive layers in the MHS Ti resulted in the suppression of cracking, whereas the monolithic nanograined (NG) Ti exhibited sub-surface cracks at the boundary of the plastic strain field. Finite element models with discrete layers and mechanically graded layersrepresenting the MHS system confirmed the absence of cracking and revealed a 38% decrease in shear stress in the sub-surface plastic strain field, compared to the monolithic NG Ti. Further, the mechanical gradation achieves a more gradual stress distribution which mitigates the interface failure and increases the interfacial toughness, thus providing strong resistance to loading damage. © 2014 Elsevier Ltd.

Anisotropic hardening model based on non-associated flow rule and combined nonlinear kinematic hardening for sheet materials

 A material model for more effective analysis of plastic deformation of sheet materials is presented in this paper. The model is capable of considering the following aspects of plastic deformation behavior of sheet materials: the anisotropy in yielding stresses in different directions by using a quadratic yield function (based on Hill’s 1948 model and stress ratios), the anisotropy in work hardening by introducing non-constant flow stress hardening in different directions, the anisotropy in plastic strains in different directions by using a quadratic plastic potential function and non-associated flow rule (based on Hill’s 1948 model and plastic strain ratios, r-values), and finally some of the cyclic hardening phenomena such as Bauschinger’s effect and transient behavior for reverse loading by using a coupled nonlinear kinematic hardening (so-called Armstrong-Frederick-Chaboche model). Basic fundamentals of the plasticity of the model are presented in a general framework. Then, the model adjustment procedure is derived for the plasticity formulations. Also, a generic numerical stress integration procedure is developed based on backward-Euler method (so-called multistage return mapping algorithm). Different aspects of the model are verified for DP600 steel sheet. Results show that the new model is able to predict the sheet material behavior in both anisotropic hardening and cyclic hardening regimes more accurately. By featuring the above-mentioned facts in the presented constitutive model, it is expected that more accurate results can be obtained by implementing this model in computational simulations of sheet material forming processes. For instance, more precise results of springback prediction of the parts formed from highly anisotropic hardened materials or that of determining the forming limit diagrams is highly expected by using the developed material model.

A double inclusion homogenization scheme for polycrystals with hierarchal topologies: Application to twinning in Mg alloys

The present work introduces a double inclusion elasto-plastic self-consistent (DI-EPSC) scheme for topologies in which crystals can contain subdomains (i.e. twins, etc.). The approach yields a direct coupling between the mechanical response of grains and their subdomains via a concentration relationship on mean fields derived from both the Eshelby and the Tanaka-Mori properties. The latent effect caused by twinning on the mechanical response is observed on both initially extruded and non-textured Mg alloys. For twinned grains, it is shown that deformation system activities and plastic strain distributions within twins drastically depend on the interaction with parent domains. Moreover, a quantitative study on the coupled influence of secondary slip activities on the material response is proposed. © 2014 Published by Elsevier Ltd.

Recent advances in machining of Austempered Ductile Iron to avoid machining induced microstructural phase transformation reaction

Austempered Ductile Iron (ADI) is a type of nodular, ductile cast iron subjected to heat treatments-austenitising and austempering. Whilst machining is conducted prior to heat treatment and offers no significant difficulty, machining post heat treatment is demanding and often avoided. Phase transformation of retained austenite to martensite leading to poor machinability characteristics is a common problem experienced during machining. Study of phase transformations is an investigative study on the factors-plastic strain (εp) and thermal energy (Q) which effect phase transformations during machining. The experimental design consists of face milling grade 1200 at variable Depth of Cut (DoC) range from 1 to 4 mm, coolant on/off, at constant speed, 1992 rpm and feed rate, 0.1 mm/tooth. Plastic strain (εp) and martensite content (M) at fracture point for each grade was evaluated by tensile testing. The effect of thermal energy (Q) on phase transformations was also verified through temperature measurements at DoC 3 and 1 mm using thermocouples embedded into the workpiece. Finally, the amount of plastic strain (εp) and thermal energy (Q) responsible for a given martensite increase (M) during milling was related and calculated using a mathematical function, M=f (εp, Q). The future work of the thesis involves an in-depth study on the new link discovered through this research: mathematical model relating the role of plastic strain and thermal energy in martensite formation.

Effect of martensite volume fraction on low cycle fatigue behaviour of dual phase steels: experimental and microstructural investigation

The low cycle fatigue (LCF) behaviour of a dual phase (DP) steel with different martensite volume fractions has been investigated, with particular focus on fatigue life, cyclic hardening/softening behaviour and microstructural evolution. DP steels with martensite volume fractions between 13% and 88% were produced and their monotonic and cyclic deformation behaviours evaluated. The LCF life has been examined in depth and compared with published literature. It has been concluded that, once normalised for plastic strain amplitude, the fatigue life was found to be significantly reduced by an increase in the martensite volume fraction. All alloys were observed to show some initial cyclic hardening followed by cyclic softening. Clear sub-cell formation occurred in ferrite grains irrespective of the martensite volume fraction, and it is suggested that this cell formation and martensite softening are responsible for the cyclic softening behaviour.

Effect of martensite morphology on low cycle fatigue behaviour of dual phase steels: Experimental and microstructural investigation

The low cycle fatigue (LCF) behaviour of a dual phase (DP) steel with different martensite morphologies has been investigated in the present work. DP steels with coarse martensite morphologies show inferior LCF life in comparison with fine martensite morphologies for all martensite volume fractions examined. It is suggested that this is be due to the development of larger local plastic strain concentrations in the ferrite with a coarser microstructure, compared to the finer microstructural morphology. Fatigue cracks were observed to initiate inside ferrite grains, and to preferentially propagate through the softer ferrite phase. The average sub-cell size was finer in samples with higher martensite volume fractions, but the sub-cell size was almost unaffected by the martensite morphology.

Anisotropic behavior in plasticity and ductile fracture of an aluminum alloy

Anisotropic mechanical behavior is investigated for an aluminum alloy of 6K21-IH T4 both in plastic deformation and ductile fracture. Anisotropic plastic deformation is characterized by uniaxial tensile tests of dog-bone specimens, while anisotropy in ductile fracture is illustrated with specimens with a central hole, notched specimens and shear specimens. All these specimens are cut off at every 15º from the rolling direction. The r-values and uniaxial tensile yield stresses are measured from the tensile tests of dog-bone specimens. Then the anisotropic plasticity is modeled by a newly proposed J2-J3 criterion under non-associate flow rule (non-AFR). The testing processes of specimens for ductile fracture analysis are simulated to extract the maximum plastic strain at fracture strokes as well as the evolution of the stress triaxiality and the Lode parameter in different testing directions. The measured fracture behavior is described by a shear-controlled ductile fracture criterion proposed by Lou et al. (2014. Modeling of shear ductile fracture considering a changeable cut-off value for stress triaxiality. Int. J. Plasticity 54, 56-80) for different loading directions. It is demonstrated that the anisotropic plastic deformation is described by the J2-J3 criterion with high accuracy in various loading conditions including shear, uniaxial tension and plane strain tension. Moreover, the anisotropy in ductile fracture is not negligible and cannot be modeled by isotropic ductile fracture criteria. Thus, an anisotropic model must be proposed to accurately illustrate the directionality in ductile fracture.

Numerical modeling and analysis for forming process of dual-phase 980 steel exposed to infrared local heating

A recent experiment confirmed that the infrared (IR) local heating method drastically reduces springback of dual-phase (DP) 980 sheets. In the experiment, only the plastic deformation zone of the sheets was locally heated using condensed IR heating. The heated sheets were then deformed by V-bending or 2D-draw bending. Although the experimental observation proved the merit of using the IR local heating to reduce springback, numerical modeling has not been reported. Numerical modeling has been required to predict springback and improve the understanding of the forming process. This paper presents a numerical modeling for V-bending and 2D-draw bending of DP 980 sheets exposed to the IR local heating with the finite element method (FEM). For describing the thermo-mechanical behavior of the DP 980 sheet, a flow stress model which includes a function of temperature and effective plastic strain was newly implemented into Euler-backward stress integration method. The numerical analysis shows that the IR local heating reduces the level of stress in the deformation zone, although it heats only the limited areas, and then it reduces the springback. The simulation also provides a support that the local heating method has an advantage of shape accuracy over the method to heat the material as a whole in V-bending. The simulated results of the springback in both V-bending and 2D-draw bending also show good predictions.

Experimental study of damage evolution in cuboid stirrup-confined concrete

This paper presents an experimental study on cuboid stirrup-confined concrete specimens under uniaxial monotonic loading and cyclic loading. The effects of stirrup volume ratio, stirrup yield strength, and concrete strength on damage evolution of the stirrup-confined concrete were investigated. The experimental results showed that the strength and ductility of concrete are improved by appropriate arrangement of the stirrup confinement. Firstly, with the increase of the stirrup volume ratio, the damage evolution of concrete can be relatively restrained. Secondly, higher stirrup yield strength usually leads to larger confining pressures and slower damage evolution. In contrast, higher concrete strength leads to higher brittleness, which accelerates damage evolution. Based on the experimental data, a plastic strain expression is obtained through curve fitting, and a damage evolution equation for stirrup-confined concrete is proposed by introducing a confinement factor (C). The comparisons results demonstrated that the proposed damage evolution curve can accurately describe the experimental results.

An Anisotropic Model of Damage and Unilateral Effect for Brittle Materials

This work deals with the initial applications and formulation of an aniscitropic plastic-damage constitutive model proposed for non-linear analysis of reinforced concrete structures submitted to a loading with change of the sign. The original constitutive model is based on the fundamental hypothesis of energy equivalence between real and continuous medium following the concepts of the Continuum Damage Mechanics. The concrete is assumed as an initial elastic isotropic medium presenting anisotropy, permanent strains and bimodularity (distinct elastic responses whether traction or compression stress states prevail) induced by damage evolution. In order to take into account the bimodularity, two damage tensors governing the rigidity in tension or compression regimes are introduced. Then, some conditions are introduced in the original version of the model in order to simulate the damage unilateral effect. The three-dimensional version of the proposed model is analyzed in order to validate its formulation when compared to micromechanical theory. The one-dimensional version of the model is applied in the analyses of a reinforced concrete beam submitted to a loading with change of the sign. Despite the parametric identification problems, the initial applications show the good performance of the model.

Comportamento plástico do aço inoxidável austenítico em baixa temperatura

Ensaios de tração uniaxiais foram empregados para deformar aços inoxidáveis austeníticos do tipo 304, em diferentes temperaturas abaixo da ambiente (de 77 K a 300 K). A relação entre a estabilidade da austenita e o encruamento, em função da temperatura de teste, é discutida quanto à transformação martensítica induzida por deformação e ao deslizamento de discordâncias na austenita. em curvas tensão-deformação que assumem a equação de Ludwik sigma = sigmao + képsilonn, na qual sigma é a tensão verdadeira e e a elongação plástica verdadeira, um modo conveniente para analisar o encruamento é por meio do diagrama log dsigma / dépsilon versus log épsilon. O aspecto significativo é a variação da taxa de encruamento dsigma / dépsilon com a elongação plástica verdadeira nas diferentes temperaturas. As mudanças no comportamento do encruamento motivando até três estágios de deformação são associadas a diferentes processos microestruturais. A transformação martensítica pode ser considerada como um processo de deformação que compete com o processo usual de deslizamento. A investigação desses estágios, na região plástica, produz uma referência qualitativa de como diferentes fatores, tais como o grau de deformação, temperatura e composição química da austenita, afetam a transformação austenita-martensita.

Experimental investigation into the effect of stress on dissolution and growth of very soluble brittle salts in aqueous solution

Das Studium der Auflösungs- und Wachstumsprozesse an Feststoff-Flüssigkeits-Grenzflächen unter nicht-hydrostatischen Beanspruchungen ist wesentlich für das Verständnis von Defor-mationsprozessen, die in der Erde ablaufen. Unter diesen genannten Prozessen gehört die Drucklösung zu den wichtigsten duktilen Deformationsprozessen, von der Diagenese bishin zur niedrig- bis mittelgradigen metamorphen Bedingungen. Bisher ist allerdings wenig darüber bekannt, welche mechanischen, physikalischen oder chemischen Potentialenergie-Gradienten die Drucklösung steuern. I.a. wird angenommen, daß die Drucklösung durch Un-terschiede kristallplastischer Verformungsenergien oder aber durch Unterschiede der Normal-beanspruchung an Korngrenzen gesteuert wird. Unterschiede der elastischen Verformungs-energien werden dabei allerdings als zu gering erachtet, um einen signifikanten Beitrag zu leisten. Aus diesem Grund werden sie als mögliche treibende Kräfte für die Drucklösung vernachlässigt. Andererseits haben neue experimentelle und theoretische Untersuchungen gezeigt, daß die elastische Verformung in der Tat einen starken Einfluß auf Lösungs- und Wachstumsmechanismen von Kristallen in einer Lösung haben kann. Da die in der Erdkruste vorherrschenden Deformationsmechanismen überwiegend im elastischen Verformungsbereich der Gesteine ablaufen, ist es sehr wichtig, das Verständnis für die Effekte, die die elastische Verformung verursacht, zu erweitern, und ihre Rolle während der Deformation durch Drucklösung zu definieren. Die vorliegende Arbeit beschäftigt sich mit Experimenten, bei denen der Effekt der mechanisch kompressiven Beanspruchung auf Lösungs- und Wachstumsprozesse von Einzelkristallen unterschiedlicher, sehr gut löslicher, elastisch/spröder Salze untersucht wurde. Diese Salze wurden als Analoga gesteinsbildender Minerale wie Quarz und Calcit ausgewählt. Der Einfluß von Stress auf die Ausbildung der Oberflächenmikrostrukturen in einer untersättigten Lösung wurde an Kaliumalaun untersucht.Lösungsrillen (20 – 40 µm breit, 10 – 40 µm tief und 20 – 80 µm Abstand) entwickelten sich in den Bereichen, in denen die Beanspruchung im Kristall am größten war. Sie verschwanden wieder, sobald der Kristall entlastet wurde. Diese Rillen entwickelten sich parallel zu niedrig indizierten kristallographischen Richtungen und sub-perpendikular zu den Trajektorien, die der maximalen, lokalen kompressiven Beanspruchung entsprachen. Die Größe der Lösungsrillen hing von der lokalen Oberflächenbeanspruchung, der Oberflächenenergie und dem Untersättigungsgrad der wässrigen Lösung ab. Die mikrostrukturelle Entwicklung der Kristalloberflächen stimmte gut mit den theoretischen Vorhersagen überein, die auf den Modellen von Heidug & Leroy (1994) und Leroy & Heidug (1994) basieren. Der Einfluß der Beanspruchung auf die Auflösungsrate wurde an Natriumchlorat-Einzelkristallen untersucht. Dabei wurde herausgefunden, daß sich gestresste Kristalle schneller lösen als Kristalle, auf die keine Beanspruchung einwirkt. Der experimentell beobachtete Anstieg der Auflösungsrate der gestressten Kristalle war ein bis zwei Größenordnungen höher als theoretisch erwartet. Die Auflösungsrate stieg linear mit dem Stress an, und der Anstieg war um so größer, je stärker die Lösung untersättigt war. Außerdem wurde der Effekt der Bean-spruchung auf das Kristallwachstum an Kaliumalaun- und Kaliumdihydrogenphosphat-Ein-zelkristallen untersucht. Die Wachstumsrate der Flächen {100} und {110} von Kalium-alaun war bei Beanspruchung stark reduziert. Für all diese Ergebnisse spielte die Oberflächenrauhigkeit der Kristalle eine Schlüsselrolle, indem sie eine nicht-homogene Stressverteilung auf der Kristalloberfläche verursachte. Die Resultate zeigen, daß die elastische Verformung eine signifikante Rolle während der Drucklösung spielen kann, und eine signifikante Deformation in der oberen Kruste verursachen kann, bei Beanspruchungen, die geringer sind, als gemeinhin angenommen wird. Somit folgt, daß die elastische Bean-spruchung berücksichtigt werden muß, wenn mikrophysikalische Deformationsmodelle entwickelt werden sollen.