Dislocation Density Evolution Research Articles

Mechanistic Origin of Ductility in Precipitation Hardening AlMgScZr Alloys

Precipitation hardening is the most effective strategy to enhance the mechanical properties of metals. Dislocation mechanisms to control strengthening during precipitation have been demonstrated extensively. However, owing to the complexity of different precipitates in alloys, variations in ductility caused by precipitation are very complex and have not been clarified so far. In this study, the effects of precipitation on ductility in precipitation hardening aluminium alloys are investigated based on a modified dislocation-based approach and experimental characterisation. The AlMgScZr alloy with spherical Al3(Sc, Zr) precipitates is used as a model alloy system to understand the effects of precipitation on ductility. Via heat treatment, shearable and non-shearable Al3(Sc, Zr) precipitates are introduced in the AlMg matrix. The results show that the ductility of AlMgScZr alloy decreases when shearable precipitates occur, while it increases during the shearable–non-shearable transition. The variation in ductility is mainly controlled by the dynamic recovery rate of the dislocations. This dislocation mechanism is supported by analysing the different precipitation–dislocation interactions and evaluating the dislocation density evolution during deformation. This study reveals the dislocation mechanism for controlling ductility during precipitation, which can provide a theoretical foundation for the design of high-performance structural materials.

Data-Driven Constitutive Model for the Inelastic Response of Metals: Application to 316H Steel

Predictions of the mechanical response of structural elements are conditioned by the accuracy of constitutive models used at the engineering length-scale. In this regard, a prospect of mechanistic crystal-plasticity-based constitutive models is that they could be used for extrapolation beyond regimes in which they are calibrated. However, their use for assessing the performance of a component is computationally onerous. To address this limitation, a new approach is proposed whereby a surrogate constitutive model (SM) of the inelastic response of 316H steel is derived from a mechanistic crystal plasticity-based polycrystal model tracking the evolution of dislocation densities on all slip systems. The latter is used to generate a database of the expected plastic response and dislocation content evolution associated with several instances of creep loading. From the database, a SM is developed. It relies on the use of orthogonal polynomial regression to describe the evolution of the dislocation content. The SM is then validated against predictions of the dead load creep response given by the polycrystal model across a range of temperatures and stresses. When the SM is used to predict the response of 316H during complex non monotonic loading, extrapolating to new loading conditions, it is found that predictions compare particularly well against those from the physics-based polycrystal model.

Evolution of dislocation and twin densities in a Mg alloy at quasi-static and high strain rates

The present work, for the first time, quantitatively studies the evolution of both dislocations and deformation twins with various strain rates in an ATZ311 Mg alloy. Interrupted tensile tests were performed at the strain rates of 0.001, 1 and 600 s−1. Deformation twins were characterized by microscopy techniques and evaluated using the fractions of twin boundaries and twinned area. The average dislocation density and the relative fractions of dislocations with different Burgers vectors were determined from neutron diffraction data. It was found that the twin fraction increases remarkably and becomes saturated at lower strain rates (0.001-1 s−1), while the dislocation density only obtains an obvious enhancement at a much higher strain rate (600 s−1). Besides, the distinctively high flow stress at high strain rate leads to a substantial increase in the density of the hard-to-activate 〈c+a〉-type dislocations, after the 〈a〉-type dislocation density reaches rapidly its saturated value at a small strain level. The twinning modes with opposite polarities are able to coexist in the same grains because of the high local stress concentration at strain rates above 1 s−1.

Application of an Incremental Constitutive Model for the FE Analysis of Material Dynamic Restoration in the Rotary Tube Piercing Process.

In the numerical simulation of hot forming processes, the correct description of material flow stress is very important for the accuracy of the results. For complex manufacturing processes, such as the rotary tube piercing (RTP), constitutive laws based on both power and exponential mathematical expressions are commonly used due to its inherent simplicity, despite the limitations that this approach involves, namely, the use of accumulated strain as a state parameter. In this paper, a constitutive model of the P91 steel derived from the evolution of dislocation density with strain, which takes into account the mechanisms of dynamic recovery (DRV) and dynamic recrystallization (DRX), is proposed for the finite element (FE) analysis of the RTP process. The material model is developed in an incremental manner to allow its implementation in the FE code FORGE®. The success of this implementation is confirmed by the good correlation between results of the simulation and experimental measurements of the manufactured tube (elongation, twist angle, mean wall thickness and eccentricity). In addition, this incremental model allows addressing how the restoring mechanisms of DRV and DRV occur during the RTP process. The analysis puts into evidence that DRV and DRX prevail over each other cyclically, following an alternating sequence during the material processing, due mainly to the effect of the strain rate on the material.

On the thermo-mechanical theory of field dislocations in transient heterogeneous temperature fields

A strong coupling between the field theory of dislocation mechanics and heat conduction is proposed. The novel model, called the Thermal Field Dislocation Mechanics (T-FDM) model, is designed to study the dynamics of dislocations during rapid or gradual temperature changes in a body having a heterogeneous temperature distribution; for example, such conditions occur in a heat-affected crystalline solid during an additive manufacturing process. Thermal strains are uniquely separated into compatible and incompatible components via the Stokes-Helmholtz decomposition and the curl of the incompatible part of thermal strains is directly related to the areal dislocation density tensor. A dislocation density evolution (including transport) law is developed and shown to be related to the evolution of the curl of incompatible thermal strains. This relationship demonstrates that dislocation generation, annihilation, motion and/or interactions with other defects can be triggered due to transient temperature changes, and conversely an evolving dislocation density induces temperature changes. The model development is completed with constitutive laws derived from energetic and dissipative considerations. The advantages and consequences of the assumptions of the T-FDM model under rapidly changing temperatures, both spatially and temporally, are discussed. The T-FDM model is intended for application at the length scale where individual dislocations can be characterized. At this level, local thermodynamic equilibrium is found to be a reasonable assumption even for high rates of change of temperature such as those occurring during an additive manufacturing process. Some illustrative examples are presented to demonstrate the applicability of the model and to better understand some of the novel concepts proposed in this work.

Evaluation of hydrogen trapping and diffusion in two cold worked CrMo(V) steel grades by means of the electrochemical hydrogen permeation technique

Hydrogen diffusion kinetics, which is influenced by the hydrogen trapping and de-trapping phenomena within the steel microstructure, plays an important role on the behaviour of steel components under hydrogen environments. Hence, the complex interaction between hydrogen atoms and steel microstructure must be analyzed in order to discuss the impact of hydrogen on the structural damage.Quenched and tempered low-alloy ferritic steels from the Cr-Mo family, with and without vanadium, have been subjected to different plastic deformation ratios by cold rolling. Dislocation densities have been determined by the analysis of the peak broadening on X-Ray diffractograms. Hydrogen diffusion kinetics was characterized by means of hydrogen permeation transients. In addition, binding energies between hydrogen atoms and microstructure were also determined using thermal desorption analysis (TDA). The analysis of the results highlights the influence of dislocations density and vanadium carbides on the hydrogen diffusion kinetics. In the 2.25Cr1Mo steel grade, hydrogen apparent diffusion coefficient decreased after the cold-work due to the increase in the density of traps (mainly related to dislocation core, ΔETL = 55–60 kJ/mol). Nevertheless, after 10% of plastic deformation, apparent diffusion coefficient ‘saturates’ according to the ‘plateau’ determined in the dislocation density evolution at higher deformation levels. Due to the vanadium addition (+0.31%), hydrogen apparent diffusion coefficient was notably reduced (compared to that obtained in the V-free steel grade). Hydrogen trapping and diffusion are the result of the interplay between vanadium carbides (ΔETL = 35 kJ/mol) and dislocation core.

The effect of grain boundary structures on crack nucleation in nickel nanolaminated structure: A molecular dynamics study

Molecular dynamics (MD) simulations were performed to explore the structures, energies and tensile properties of grain boundaries (GBs) as well as crack nucleation in nickel nanolaminated (Ni NL) structures. Four typical textures observed in experiments (Liu et al., 2013) [6] were considered in this paper. Results showed that low-angle GBs consist of a series of periodically arranged dislocations while high-angle GBs are composed of disordered phase for all textures. GB energies increase linearly with increasing misorientation in the range of low-angle GBs (0–10°). Then, the growth rate of energies slows down and finally stabilizes when the misorientation angle reaches 30°. Among four textures, {111} 〈110〉 texture has the highest GB energy while {110} 〈111〉 texture the lowest one. The tensile properties of NL structures with different textures and misorientations were further investigated. Results showed that the tensile properties depend primarily on textures, while weakly on GB energies and dislocation densities. {111} 〈112〉 texture possesses the best combination of high-strength and ductility among the four textures. Furthermore, the evolution of dislocation density and structure as well as the nucleation of crack were analysed. Crack nucleates at the junction between Shockley partial dislocations and twin boundaries generated during deformation for low-angle GBs, while at the location where Shockley partial dislocations and the original disordered GBs intersect for high-angle GBs. Our results provide a fundamental understanding of GB structures and deformation mechanisms of Ni NL structures.

Damage and strengthening mechanisms in severely deformed commercially pure aluminum: Experiments and modeling

The current investigation presents a breakdown analysis of the elastoplastic behavior of commercially pure aluminum pre-strained via severe plastic deformation (SPD) and tested in tension. The tensile samples selected, owing to their prior SPD, had the gradient microstructure from the fragmentation stage as well as a homogeneous equiaxed structure from the steady-state regime. Except for the regions of low deformation and steady-state of SPD, the microstructures of pre-strained material were largely dominated by the presence of geometrically necessary boundaries. During tensile straining, dislocation strengthening contributed more to the overall material strength in fragmentation stage samples, while grain boundary strengthening played a major role in the steady-state stage samples. The dislocation density evolution rate-based approach predicted a more active role for the dynamic annihilation/recovery events in the SPD material when compared to the fully recrystallized condition. This could explain the drastic drop in tensile elongation of the pre-strained material as well as the enhancement in uniform and post-necking elongation with the gradual increase in the amount of pre-strain. A plastic instability condition based on the dislocation density evolution approach successfully accounted for the observed stable deformation limits in the coarse- and fine-grained material.

Effects of pre-strain and stress level on stress relaxation ageing behaviour of 2195 Al–Li alloy: Experimental and constitutive modelling

In the present work, the stress relaxation behaviour, mechanical properties and microstructural evolution of 2195 Al–Li alloy with different pre-strains (0%, 2% and 4%) have been experimentally investigated under different initial stress levels at 180 °C for 16 h. It is found that pre-strain can extend the duration of the first stress relaxation stage and significantly promote the stress reduction. Meanwhile, a new “multi-step stage” stress relaxation feature, containing a particular linear relaxation stage, is observed for the 2195 Al–Li alloy during stress relaxation ageing (SRA) process. In addition, the tensile strength of the alloy increases with the increase of pre-strains and initial stresses, while the corresponding elongation is opposite. The evolution of precipitates, including G.P. Zones, θ″, θ′ and T1 phases, have been characterized by transmission electron microscope (TEM). The number of T1 phases increases with the increase of the pre-strains and initial stresses, while the number of θ′ phases gradually decreases. Based on precipitation kinetics, stress relaxation mechanism and dislocation theory, a physically-based SRA constitutive model considering the evolution of dislocation density and relative volume fraction of T1 and θ′ precipitates is established. The results calculated by the constitutive model are in good agreement with the experimental data.

Porous polycrystal plasticity modeling of neutron-irradiated austenitic stainless steels

A micromechanical model for quantifying the simultaneous influence of irradiation hardening and swelling on the mechanical stiffness and strength of neutron-irradiated austenitic stainless steels is proposed. The material is regarded as an aggregate of equiaxed crystalline grains containing a random dispersion of pores (large voids due to large irradiation levels) and exhibiting elastic isotropy but viscoplastic anisotropy. The overall properties are obtained via a judicious combination of various bounds and estimates for the elastic energy and viscoplastic dissipation of voided crystals and polycrystals. Reference results are generated with full-field numerical simulations for dense and voided polycrystals with periodic microstructures and crystal plasticity laws accounting for the evolution of dislocation and Frank loop densities. These results are calibrated with experimental data available from the literature and are employed to assess the capabilities of the proposed model to describe the evolution of mechanical properties of highly irradiated Solution Annealed 304L steels at 330oC. The agreement between model predictions and simulations is seen to be quite satisfactory over the entire range of porosities and loadings investigated. The expected decrease of overall elastic properties and strength for porosities observed at large irradiation levels is reported. The mathematical simplicity of the proposed model makes it particularly apt for implementation into finite-element codes for structural safety analyses.

The low-stress and high-temperature creep in LiF single crystals: An explanation for the So-called Harper-Dorn creep

The theory of creep behavior in single and poly-crystalline materials at very low-stresses and at very high temperatures as originally proposed by Harper and Dorn has been under constant debate since its proposition. Accordingly, the principal objectives of this work are to study the creep behavior of high purity single crystals of LiF in the Harper-Dorn regime, which has never been studied. It is observed that stress exponent for LiF at 0.95 Tm changes from ~3.5 (“five”-power law) to ~1.5 at stresses below 10−5 G, which is typical transition stress for the Harper-Dorn creep in other materials. The evolution of dislocation density at very high temperatures (~0.92 Tm) under static annealing conditions reveals a saturation of the dislocation density after ~150 h up to 10,000 h. Furthermore, the dislocation density in the Harper-Dorn regime remains independent of the applied stress, with a value only slightly higher than the saturation dislocation density measured under static annealing conditions. Thus, the typical constant dislocation density observed in the Harper-Dorn regime may be a consequence of “frustration” of the Frank network in LiF, just as concluded in our Al work at very low stresses. If the initial dislocation density is lower than the frustration value, then the “five”-power law creep is expected. A unified dislocation-network based model is developed to interpret the creep response of LiF in the Harper-Dorn and “five”-power law regimes.

Forming limits of magnesium alloy AZ31B sheet at elevated temperatures

Magnesium alloy sheets usually has to be processed by warm forming, and change of strain path and evolution of microstructure can significantly influence their warm formability. Forming limit test for an AZ31B alloy sheet under strain path changes was configured and implemented, and the effects of strain paths and microstructure evolution on the forming limit diagram are investigated. The sheet was pre-strained under in-plane uniaxial, plane strain and biaxial tension loading paths at 150 °C, 200 °C and 300 °C, followed by hemispherical punch stretching experiments at the three temperatures using specimens extracted from the pre-strained samples. A crystal plasticity model that incorporates dynamic recrystallization (DRX) and annealing recovery was combined with the Marciniak-Kuczyński (M-K) approach to calculate the FLDs. The evolution of dislocation density during annealing in the pre-strained FLD test at 200 °C was evaluated, through which the predictions of pre-strained FLDs were considerably improved. The present work provides experimental as well as crystal plasticity based methods for evaluating warm formability of magnesium alloys influenced by temperature, pre-straining, DRX and recovery.

Enhancement of grain structure and mechanical properties of a high-Mn twinning-induced plasticity steel bearing Al–Si by fast-heating annealing

In this study, a cold-rolled Fe-0.01C-21.3Mn–3Al–3Si (wt.%) TWIP steel was undergone a fast-heating (FH) annealing at high temperatures of 1000–1200 °C and 2 s soaking time for grain refinement and controlling the phase structure and thereby to enhance the mechanical properties. For comparison, recrystallization annealing was conducted at lower temperatures of 650 and 700 °C for 180 s. The microstructural evolution of the FH annealed steel was surveyed using electron backscatter diffraction. The strain hardening behavior of the FH structures was studied by tensile tests. The tensile flow curves were also predicted by a phenomenological model based on the evolution of dislocation density during deformation. Fine mainly austenitic structure was promoted by FH annealing at 1000 and 1100 °C. At the lower temperatures of 650 and 700 °C, bands of finer grains, indicative of some inhomogeneity, were evident in the mostly austenitic recrystallized microstructure. However, at 1200 °C, the structure consisted of coarse austenite and ferrite with almost equal fractions. The FH annealed structures exhibited a remarkable improvement in the mechanical properties (a better combination of yield and tensile strength and ductility) compared to conventional long annealing cycles.

Anisotropy in creep ageing behavior of textured Al-Cu alloy under different stress states

Deformation and properties are both important factors in understanding creep ageing behavior, especially for textured alloys subjected to a complex stress-state. Creep deformation and tensile properties of a textured Al-Cu alloy after tension and compression creep tests were evaluated at different orientations with respect to the rolling directions. From these observations, the in-planar anisotropy (IPA) of creep deformation and yield strength were calculated and correlated with textures and microstructures of the alloy. It has been found that the creep strain after tension and compression creep tests are largest when the applied stress is along the rolling direction (RD) and smallest when the applied stress is along the transverse direction (TD). The as-received alloy has obvious in-planar anisotropy of yield strength, but this anisotropy basically disappeared after ageing. The different stress states cause different creep mechanisms and also affect the evolution of dislocation density. It was found that the dislocation density is highest when the tensile stress is applied along the TD, while the dislocation density in different stress orientations is basically the same under compressive stress. This should be the main reason that the IPA of creep strain after compression creep test (25.4%) is greater than that after tension creep test (15.0%).

Multiscale simulation of grain refinement induced by dynamic recrystallization of Ti6Al4V alloy during high speed machining

During high speed machining (HSM), the strong thermal-mechanical coupling can lead to the microstructure evolution in the deformation zone of workpiece. Grain refinement may occur, which has great effects on the mechanical behavior, and even on the fatigue strength and corrosion resistance of the machined surface. The development of multiscale models to predict the microstructure evolution is gaining rising interest. This study aims to investigate the grain refinement induced by dynamic recrystallization (DRX) occurring in HSM of Ti6Al4V, through finite element (FE) and cellular automata (CA) methods. An orthogonal cutting model for HSM of Ti6Al4V is developed combining a modified Johnson-Cook constitutive model (TANH) and Johnson-Mehl-Avrami-Kolmogorov (JMAK) DRX model. The CA model is proposed considering dislocation density evolution, grain nucleation and growth. The 2D mesoscopic microstructure evolution is simulated successfully by the CA model in which the input deformation parameters come from the FE simulations of the orthogonal cutting process. Finally, the grain size and microstructure morphology calculated by both FE and CA methods are compared with those characteristics obtained experimentally by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Identical microstructure predictions from both CA and FE methods show a reasonable agreement with the TEM results, on the condition that twinning and phase transformation are not considered in the simulations. This work proves that the combination of FE and CA methods is an effective approach to achieve a more comprehensive understanding of the microstructure evolution and its effect on mechanical behavior during HSM. It shows that the rise of both DRX volume fraction and DRX grain size finally results in the slightly decreasing of average grain size of serrated chips with the increase of cutting speed, which leads to the strain softening phenomenon of flow stress.

Dynamics of growth and collapse of nanopores in copper

Variation of pore size is relevant for both the growth of voids during fracture and the compaction of pores at compression of a porous medium. In this work we examine the previously proposed continuum model of dislocation-stimulated growth of nanovoids in Al to the case of Cu for both tension and compression of the sample with a previously cut pore. Results of continuum model are verified and parameters are fitted using the molecular dynamics(MD) simulations. Dependencies of surface tension and energy of dislocation formation on temperature are obtained from fitting procedure. Continuum model allows one to adequately describe the evolution of pressure, pore radius and dislocation density with time during both tension and compression in the MD system.

Simulation of Grain Refinement Induced by High-Speed Machining of OFHC Copper Using Cellular Automata Method

Abstract During high-speed machining (HSM), the microstructure of materials evolves with significant plastic deformation process under high strain rate and high temperature, which affects chip formation and material fracture mechanisms, as well as surface integrity. The development of models and simulation methods for grain refinement in machining process is of great importance. There are few models which are developed to predict the evolution of the grain refinement of HSM in mesoscale with sufficient accuracy. In this work, a cellular automata (CA) method with discontinuous (dDRX) and continuous (cDRX) dynamic recrystallization (DRX) mechanisms is applied to simulate the grain refinement and to predict the microstructure morphology during machining oxygen-free high-conductivity (OFHC) copper. The process of grain evolution is simulated with the initial conditions of strain, strain rate, and temperature obtained by finite element (FE) simulation. The evolution of dislocation density, grain deformation, grain refinement, and growth are also simulated. Moreover, cutting tests under high cutting speeds (from 750 m/min to 3000 m/min) are carried out and the microstructure of chips is observed by electron backscatter diffraction (EBSD). The results show a grain refinement during HSM, which could be due to the occurrence of dDRX and cDRX. High temperature will promote grain recovery and growth, while high strain rate will significantly cause a high density of dislocations and grain refinement. Therefore, HSM contributes to the fine equiaxed grain structure in deformed chips and the grain morphology after HSM can be simulated successfully by the CA model developed in this work.

Viscoplastic constitutive equations for modeling fluid loading and damage evolution during warm medium forming

A unified viscoplastic constitutive model is proposed coupling fluid pressure rate control and damage evolution for warm medium forming (WMF), which also includes flow stress function, hardening law and dislocation density evolution. The pressure rate and damage behavior are investigated based on the experimental data of Ref. (Lang et al., 2013) [10] and the fracture morphology observations of specimens. The constitutive equations are discretized and derived through the fourth-order Runge-Kutta method. Meanwhile, the material constants of this model are determined using the Genetic Algorithm. The proposed constitutive model is applied to the WMF process of AA7075-O sheet and compared with the results of Ref. [10]. The error between calculated and experimental data is quantified using the average absolute relative error (AARE). Results indicate that the prediction accuracy of the proposed constitutive model is significantly improved compared with Ref. [10], also, the predictions compare well with the experimental results. The new constitutive model can effectively predict the flow behavior of AA7075-O in WMF.

Atomic simulation of crystal orientation effect on coating surface generation mechanisms in cold spray

Cold spray (CS) as a new surface modification method is widely applied in improving surface quality. The effect of crystal orientation of powder particles on coating surface generation mechanisms in cold spray is systematically investigated by molecular dynamics (MD) simulations in this work. The amorphization tendency and temperature distribution in the jetting region in our simulation are consistent with previous experimental results. In particular, our results show that crystal orientation affects the interactions between the powder particles and the surface of the substrate dramatically, leading to different atomic stress distribution, dislocation density evolution and microstructure evolution processes in the particle/substrate interface region for powder particles with different crystal orientations. The coating surface generation mechanism related to the slip plane system will be discussed.

On the Evidence of Thermodynamic Self-Organization during Fatigue: A Review.

In this review paper, the evidence and application of thermodynamic self-organization are reviewed for metals typically with single crystals subjected to cyclic loading. The theory of self-organization in thermodynamic processes far from equilibrium is a cutting-edge theme for the development of a new generation of materials. It could be interpreted as the formation of globally coherent patterns, configurations and orderliness through local interactivities by “cascade evolution of dissipative structures”. Non-equilibrium thermodynamics, entropy, and dissipative structures connected to self-organization phenomenon (patterning, orderliness) are briefly discussed. Some example evidences are reviewed in detail to show how thermodynamics self-organization can emerge from a non-equilibrium process; fatigue. Evidences including dislocation density evolution, stored energy, temperature, and acoustic signals can be considered as the signature of self-organization. Most of the attention is given to relate an analogy between persistent slip bands (PSBs) and self-organization in metals with single crystals. Some aspects of the stability of dislocations during fatigue of single crystals are discussed using the formulation of excess entropy generation.