Plastic Strain Heterogeneities Research Articles

Criterion for void nucleation by particle debonding in metals obtained from molecular dynamics simulations

The critical conditions for void nucleation by particle debonding at a θ-particle in an aluminum matrix are identified through a comprehensive set of molecular dynamics simulations spanning a range of stress triaxialities and Lode parameter values. Specifically, it is determined that nucleation occurs when the local normal stress at the matrix–particle interface reaches a critical value of 8.14 GPa. When plasticity occurs in the matrix prior to nucleation, an additional plastic stress concentration is observed as a result of the plastic strain build up around the particle. Our results indicate that this plastic stress concentration factor increases roughly linearly with equivalent plastic strain, independent of triaxiality and Lode parameter. Comparing our results with the literature, we observe a much stronger influence of plastic strain than is predicted by continuum plasticity theory. We argue that this difference derives from the fact that nucleation is fundamentally driven by local stress hot spots resulting from the heterogeneity of plastic strain, while continuum theory is based on homogenized plastic strain fields. These results provide guidance for development of ductile fracture engineering models, while giving a warning regarding the use of continuum theory to predict damage initiation phenomena in metals.

Interactions between plastic deformation and precipitation in Aluminium alloys: A crystal plasticity model

This work presents a crystal plasticity model for dynamic precipitation in aluminium alloys. It takes into account both the influence of an evolving precipitate distribution on the critical stress for dislocation glide, and the accelerating effect of deformation on precipitation kinetics. The effect of precipitates on deformation behaviour is integrated into the crystal plasticity constitutive law. The effect of deformation on precipitation kinetics is modelled spatio-temporally using a multi-class precipitation kinetic model (KWN) incorporating the effect of deformation through accelerated solute diffusion caused by the production of excess vacancies. The model is applied to growth and coarsening of shearable precipitates in pre-aged AA7075 alloy under deformation at 150°C, which corresponds to an industrially relevant production. This paper first explores the influence of dynamic precipitation on the tensile behaviour, showing that dynamic precipitation might be responsible for a gain in uniform elongation and tensile stress of respectively 2% strain and 50 MPa for the case at hand. The influence of dynamic precipitation on the development of plastic strain heterogeneities is discussed. The model demonstrates how spatial heterogeneities in precipitate distribution may develop during deformation, and how these heterogeneities correlate with the development of strain heterogeneities. The precipitate distributions obtained under static or dynamic ageing are predicted and compared with each other, and the influence of texture is discussed.

Continuum modeling of dislocation channels in irradiated metals based on stochastic crystal plasticity

As a common feature observed in irradiated metallic materials, the formation of dislocation channels has been extensively studied and is considered to play a key role in irradiation embrittlement. However, modeling dislocation channels with the conventional crystal plasticity theory has been a theoretical challenge due to the difficulty of capturing microstructural inhomogeneities. Here a continuum crystal plasticity framework incorporating a stochastic distribution model of critical resolved shear stress (CRSS) is developed to describe the formation of dislocation channels and further plastic flow localization in irradiated materials. We show that the stochastic model is capable of capturing the heterogeneity of microscale plastic strain, which is an inherent feature of metallic materials during plastic deformation. It acts as an important microscale perturbation to trigger the dislocation channel nucleation in irradiated metals, especially for single crystals that lack mesoscale perturbations such as intergranular incompatibility and grain anisotropy. Without predetermining the potential nucleation position of dislocation channels, the stochastic irradiation crystal plasticity framework successfully simulates the dislocation channel formation and plasticity localization in both irradiated single- and polycrystalline copper (Cu), and further indicates the irradiation defect density threshold for the dislocation channel formation. This stochastic model broadens the application of the conventional crystal plasticity framework, and might provide new insights for other studies on plasticity localization, including shear bands formation of metals, mechanical behaviors with heterogeneous deformation and so on.

Dislocation-density based crystal plasticity model with hydrogen-enhanced localized plasticity in polycrystalline face-centered cubic metals

Hydrogen-enhanced localized plasticity (HELP) has been recognized as an important mechanism for hydrogen embrittlement. Two recognized explinations have been proposed for HELP. The first one is the elastic shielding theory, in which the elastic stress field of solute hydrogen weakens the interactions between dislocations. Another one is the Gibbs theory of absorption isotherm: the lowered dislocation line energy by segregated hydrogen is considered as the main reason. In this work, a dislocation-density based crystal plasticity framework concerning the explicit incorporation of the dislocation line energy is proposed. The explicit consideration of dislocation line energy leads the way to the modelling of HELP mechanism according to the Gibbs theory of absorption isotherm. It is shown that the experimentally observed hydrogen-reduced activation volume and total activation free energy in thermally activated forest intersection in face-centered cubic (FCC) metals can be easily attributed to the reduction of dislocation line energy in the hydrogen environment. Finite element calculations of tensile tests for polycrystalline Pd-H and Ni-H alloys capture several important hydrogen-affected plasticity behaviors: hydrogen-increased flow stress, hydrogen-enhanced dislocation multiplication, hydrogen-promoted heterogeneity of plastic strain and hydrogen-delayed exhaustion of mobile dislocations, which can be all attributed to hydrogen reduced dislocation line energy in the present model. Besides, the influences of hydrogen-reduced vacancy formation free energy and stacking fault energy on thermal annihilation are also considered. However, the simulation results show that they are less important compared with hydrogen-reduced dislocation line energy. The present work is essential for further physically-based modeling of hydrogen distribution in polycrystals and hydrogen-induced damage and failure.

Surface patterning for combined digital image correlation and electron backscatter diffraction in-situ deformation experiments

A considerable amount of information can be gained from combined collection of both digital image correlation (DIC) measurements, and of electron backscattered diffraction (EBSD) data from the same area during in-situ deformation experiments. Such data collection remains a challenge, however, due the influence of the surface markers required for DIC on the EBSD data quality. In this work we demonstrate that by careful control of the sample preparation process, a two-step electropolishing method can be used to generate excellent surface markers for DIC where the markers are integral features on the surface. The method does not require any special equipment and can be used to collect high quality EBSD data and DIC data with sub-micron resolution on the same area during repeated loading as part of in-situ deformation experiments. Combined EBSD and DIC measurements are illustrated in this work for samples of Al deformed in tension to a strain of 10%. Due to the integral nature of the surface markers we demonstrate also that it is possible to perform DIC measurements up to large plastic strains, including the necked region within a tensile sample. A comparison of EBSD and DIC data collected from the same area of a tensile-deformed sample shows that although the EBSD data provide excellent information on the lattice rotations developed during deformation, these data cannot be directly used as a measure of local plastic strain on the scale of the deformation microstructure. The ability to collect both EBSD and DIC data during an in-situ experiment provides, therefore, an opportunity to explore further the complex relationship between local plastic strain heterogeneity and EBSD-based measures of crystal lattice rotation.

Effect of Temperature on Strength and Hardness in Multi-pass Equal Channel Angular Pressing (ECAP) of Aluminum Alloys

In the Equal channel angular pressing (ECAP) process, the sample passes through the channel and the shear stress applied to the sample leads to grain refinement and consequently, the mechanical properties of the sample will be increased. In this article, the effect of implementing the ECAP process at elevated temperature on the strength and hardness of the samples will be studied. Commercially pure (99.0% Al) and AA6063 aluminum round bars are prepared and ECAPed in a die with channel angle of $$\phi$$ = 120° and a corner angle of $$\varphi$$ = 20°. The tensile strength and hardness are compared for 1–8 pass ECAPed samples at 150 °C and room temperature. Also, the ECAP process is modeled in a finite element software to predict the plastic strain distribution in repetitive passes of ECAP. The results show that performing ECAP at elevated temperature decreases the tensile strength by about 5% and 12% in the AA6063 and commercially pure aluminum alloy samples, respectively. Also, at 150 °C, the percent of the increase in the tensile strength decreases in pass #1 but at pass #8 of ECAP, the percent of increase in the tensile strength is equal. So, decrease in the tensile strength in initial passes cannot be compensated by repetition of the ECAP process and at higher passes the strain saturation does not allow to recompense the decrease in the strength at initial passes. The finite element results show that the plastic strain heterogeneity and the value of equivalent plastic strain obtained from FEM are comparable with analytical formulations proposed by other researchers with acceptable error.

In-situ study of microstructural evolution and local strain distribution during tensile loading of near-micrometre grain size aluminium

A combined digital image correlation (DIC) and electron backscatter diffraction (EBSD) study of local strain distribution and microstructural evolution during tensile loading has been carried on samples of near-micrometre grain size Al prepared by spark plasma sintering. To achieve the required spatial resolution and allow combined DIC and EBSD measurements a method of surface patterning using colloidal silica was developed. The DIC results reveal a wide variety in heterogeneity of plastic strain, both in terms of the average strain experienced by each grain and regarding the extent and nature of strain localization within individual grains. No obvious correlation is found between the heterogeneity in plastic strain and either Schmid factor, grain size or the pattern of local grain rotations. The experiments also allow investigation of the pattern of crystal rotation during tension in near-micrometer grain size samples and reveal differences in the mean grain rotation and the in-grain orientation spread.

Microscopic heterogeneity of plastic strain and lattice rotation in partially recrystallized copper polycrystals

Partial recrystallization of highly deformed polycrystalline aggregates creates a bimodal grain size distribution, which improves ductility while maintaining relatively high strength. In this work, the microstructure evolution during isothermal annealing of cold rolled copper samples was investigated using electron backscattered diffraction (EBSD) and the macroscopic mechanical strength of partially recrystallized samples was measured under uniaxial tension. Different models were tested in order to reproduce both the macroscopic mechanical response and the microscopic strain field inside a sample with 41% recrystallized grains loaded inside a scanning electron microscope to allow in-situ EBSD mapping. Crystal plasticity based finite element modeling (CPFEM) performed on a 2D mesh conforming to the experimental microstructure was compared to 3D predictions on an idealized model microstructure.

Microstructure and mechanical properties of laser additive repaired Ti17 titanium alloy

Abstract Laser additive manufacturing technology with powder feeding was employed to repair wrought Ti17 titanium alloy with small surface defects. The microstructure, micro-hardness and room temperature tensile properties of laser additive repaired (LARed) specimen were investigated. The results show that, cellular substructures are observed in the laser deposited zone (LDZ), rather than the typical α laths morphology due to lack of enough subsequent thermal cycles. The cellular substructures lead to lower micro-hardness in the LDZ compared with the wrought substrate zone which consists of duplex microstructure. The tensile test results indicate that the tensile deformation process of the LARed specimen exhibits a characteristic of dramatic plastic strain heterogeneity and fracture in the laser repaired zone with a mixed dimple and cleavage mode. The tensile strength of the LARed specimen is slightly higher than that of the wrought specimen and the elongation of 11.7% is lower.

Effect of composition and pressure on the shear strength of sodium silicate glasses: An atomic scale simulation study.

The elastoplastic behavior of sodium silicate glasses is studied at different scales as a function of composition and pressure, with the help of quasistatic atomistic simulations. The samples are first compressed and then sheared at constant pressure to calculate yield strength and permanent plastic deformations. Changes occurring in the global response are then compared to the analysis of local plastic rearrangements and strain heterogeneities. It is shown that the plastic response results from the succession of well-identified localized irreversible deformations occurring in a nanometer-size area. The size and the number of these local rearrangements, as well as the amount of internal deviatoric and volumetric plastic deformation, are sensitive to the composition and to the pressure. In the early stages of the deformation, plastic rearrangements are driven by sodium mobility. Consequently, the elastic yield strength decreases when the sodium content increases, and the same when pressure increases. Finally, good correlation was found between global and local stress-strain relationships, reinforcing again the role of sodium ions as local initiators of the plastic behavior observed at larger scales.

Evolution of plastic deformation and its effect on mechanical properties of laser additive repaired Ti64ELI titanium alloy

In this paper, laser additive manufacturing (LAM) technology with powder feeding has been employed to fabricate 50%LAMed specimens (i.e. the volume fraction of the laser deposited zone was set to 50%). With aid of the 3D-DIC technique, the tensile deformation behavior of 50%LAMed Ti64ELI titanium alloy was investigated. The 50%LAMed specimen exhibits a significant characteristic of strength mismatch due to the heterogeneous microstructure. The tensile fracture of 50%LAMed specimen occurs in WSZ (wrought substrate zone), but the tensile strength is slightly higher and the plastic elongation is significantly lower than that of the wrought specimen. The 3D-DIC results shows that the 50%LAMed specimen exhibits a characteristic of dramatic plastic strain heterogeneity and the maximal strain is invariably concentrated in WSZ. The ABAQUS simulation indicates that, the LDZ (laser deposited zone) can constrain the plastic deformation of the WSZ and biaxial stresses develop at the interface after yielding.

Influence of the Martensitic Transformation on the Microscale Plastic Strain Heterogeneities in a Duplex Stainless Steel

The influence of the martensitic transformation on microscale plastic strain heterogeneity of a duplex stainless steel has been investigated. Microscale strain heterogeneities were measured by digital image correlation during an in situ tensile test within the SEM. The martensitic transformation was monitored in situ during tensile testing by high-energy synchrotron X-ray diffraction. A clear correlation is shown between the plasticity-induced transformation of austenite to martensite and the development of plastic strain heterogeneities at the phase level.

Local Plastic-Strain Heterogeneities and Their Impact on the Ductility of Mg

Microscale plastic strain heterogeneity can arise in polycrystalline Mg and its alloys in a variety of different ways. In this article, we illustrate how microscale digital image correction based on scanning electron microscope images can reveal this plastic heterogeneity in commercially pure polycrystalline Mg and how such observations provide insight into plasticity, damage, and ductility.

Microscale plastic strain heterogeneity in slip dominated deformation of magnesium alloy containing rare earth

The propensity for the magnesium alloy ZEK100 to develop large microscale plastic strain heterogeneity has been quantified and correlated to microstructure using a combination of experiments and simulations. Conditions were specifically selected where deformation is dominated by slip rather than twinning. Digital image correlation measurements of intragranular plastic strain heterogeneity have revealed plastic strains as large as 5 times the macroscopic tensile strain. This strain amplification was found to be neither spatially correlated nor correlated with crystal orientation. Large local strains were, however, found to be statistically linked to proximity to grain boundaries. This suggests the importance of interactions between neighboring grains. To investigate this further full-field viscoplastic Fast Fourier Transform (VPFFT) crystal plasticity simulations were performed on synthetic microstructures representative of the material studied experimentally. It was found that both the macroscopic stress–strain response as well as the local plastic strain distribution could be well reproduced when the anisotropy in ‘hardness’ of the basal and non-basal slip systems was sufficiently high. Strain amplification was found to occur, in this case, to slip in regions of high basal slip activity adjacent to regions of high non-basal slip activity.

Plastic strain heterogeneities in an Mg–1Zn–0.5Nd alloy

The distribution of plastic strain, both intergranular and intragranular, has been evaluated using digital image correlation on a tensile-deformed Mg–1Zn–0.5Nd alloy. The intergranular strain distribution is sensitive to both the orientation of the grains and the orientations of neighbouring grains. Large intragranular strain gradients were observed close to some grain boundaries. These high levels of local strain were seen to correlate to the operation of additional slip and/or twin systems close to grain boundaries, deformation kinking and/or grain boundary sliding.

Local plastic strain inhomogeneity in a ZEK100 Mg alloy

Magnesium alloys have great potential for lightweighting applications in the transportation industry. It is known, however, that Mg and Mg-alloys exhibit large plastic strain heterogeneity. Such heterogeneity is important both from the perspective of formability and fracture if such sheet materials are to be stamped. Also, such observations are important for our fundamental understanding of how plasticity spreads in such materials. In this work we have sought to couple together local plastic strain measurements using digital image correlation with full-field crystal plasticity simulations with the idea of identifying and quantifying the plastic strain heterogeneity. A recently developed ZEK-100 alloy has been studied, as this alloy has shown promise as a wrought sheet product.

Mesoscale Simulation of Uniaxial Tension of FCC Polycrystal Using Viscoplastic Self Consistent Method

A viscoplastic self consistent model was developed using a rate sensitive constitutive relation, isotropic hardening law, and considering the interaction between the grains and their surroundings. The model was applied to simulate the mesoscopic responses of fcc polycrystalline aggregate during tensile deformation. The macro textures, the grain rotation behaviors, plastic strain and stress heterogeneities, and slip system activities were investigated. The model successfully predicts the typical tensile textures, the grain rotations toward (111) and (100) directions and the orientation dependent slip activities, etc. The simulation results are qualitatively in agreement with experimental measurements and theoretical predictions.

A multiphase mechanical model for Ti–6Al–4V: Application to the modeling of laser assisted processing

abstract A multiphase model for Ti–6Al–4V is proposed. This material is widely used in industrial applications andsoneeds accurate behaviour modeling. Tests have been performed inthe temperature range from 25 Cto1020 1C and at strain rates between 10 3 s and 1 s 1 . This allowed the identification of a multiphasemechanical model coupled with a metallurgical model. The behaviour of each phase is calibrated by solv-ing an inverse problem including a phase transformation model and a mechanical model to simulate testsunder thermomechanical loadings. A scale transition rule (b-rule) is proposed in order to represent theredistribution of local stresses linked to the heterogeneity of plastic strain. Finally this model is appliedto two laser assisted processes: direct laser fabrication and laser welding. 2009 Elsevier B.V. All rights reserved. 1. IntroductionTitanium alloys are extensively used in leading industries, dueto their low density and high specific strength (Rm/ q ) at elevatedtemperature (aeronautics, nuclear energy) and their compatibilitywith human tissues (biomedical applications). The most populartitanium alloy is Ti–6Al–4V (wt.%). This is a

Assessment of plastic heterogeneity in grain interaction models using crystal plasticity finite element method

Micromechanical models aimed at simulating deformation textures and resulting plastic anisotropy need to incorporate local plastic strain heterogeneities arising from grain interactions for better predictions. The ALAMEL model [Van Houtte, P., Li, S., Seefeldt, M., Delannay, L. 2005. Deformation texture prediction: from the Taylor model to the advanced Lamel model. Int. J. Plasticity 21, 589–624], is one of the models in which the heterogeneous nature of plastic deformation in metals is introduced by accounting for the influence of a grain boundary on the cooperative deformation of adjacent grains. This is achieved by assuming that neighbouring grains undergo heterogeneous shear rates parallel to the grain boundary. The present article focuses on understanding the plastic deformation fields near the grain boundaries and the influence of grain interaction on intra-grain deformations. Crystal Plasticity Finite Element Method (CPFEM) is employed on a periodic unit cell consisting of four grains discretised into a large number of elements. A refined study of the local variation of strain rates, both along and perpendicular to the grain boundaries permits an assessment of the assumptions made in the ALAMEL model. It is shown that the ALAMEL model imbibes the nature of plastic deformation at the grain boundaries very well. However, near triple junctions, the influence of a third grain induces severe oscillations of the stress tensor, reflecting a singularity. According to CPFEM, such singularity can lead to grain subdivision by the formation of new boundaries originating at the triple junction.

Finite element simulations of the cyclic elastoplastic behaviour of copper thin films

A large-scale computational and statistical strategy is presented to investigate the development of plastic strain heterogeneities and plasticity induced roughness at the free surface in multicrystalline films subjected to cyclic loading conditions, based on continuum crystal plasticity theory. The distribution of plastic strain in the grains and its evolution during cyclic straining are computed using the finite element method in films with different ratios of in-plane grain size and thickness, and as a function of grain orientation (grains with a {1 1 1} or a {0 0 1} plane parallel to the free surface and random orientations). Computations are made for 10 different realizations of aggregates containing 50 grains and one large aggregate with 225 grains. It is shown that overall cyclic hardening is accompanied by a significant increase in strain dispersion. The case of free-standing films is also addressed for comparison. The overall surface roughness is shown to saturate within 10 to 15 cycles. Plasticity induced roughness is due to the higher deformation of {0 0 1} and random grains and due to the sinking or rising at some grain boundaries.