Plasticity Finite Element Method Simulations Research Articles

Bending properties and deformation micromechanisms of near-α titanium alloy sheets/foils considering initial texture characteristics and size effect

Clarifying the bending deformation behaviour of metal foils is essential for meeting the lightweighting requirements of metal honeycomb structures. This study selected Ti65 alloy specimens with various thicknesses and initial α-phase textures to conduct room-temperature three-point bending experiments. A detailed comparative analysis was performed on the bending deformation behaviour of Ti65 alloy sheets and foils. It reveals that in the foil specimens, the weakening effect of surface layer grains is significant. Under the influence of size effects, the springback angle of Ti65 alloy foils with coarse α-phase grains decreases markedly. Additionally, through various methods, including global Schmid factor analysis, lattice rotation analysis, and crystal plasticity finite element method simulations, the specific relationship between α-phase texture and the bending performance of Ti65 alloy foils was thoroughly investigated. The rolling process influences the bending performance of Ti65 alloy by determining the α-phase texture. Unidirectionally rolled Ti65 alloy products exhibit a transverse α-phase texture, which predisposes them to form transverse texture α-phase macrozones during bending. In contrast, cross-directionally rolled Ti65 alloy foils possess a basal α-phase texture biased toward the transverse direction. This not only helps avoid the formation of macrozones but also ensures coordinated deformation across the foil, resulting in superior bending performance.

A crystal plasticity model of Dynamic Strain Aging for a near-[formula omitted] Ti-alloy

Timetal-834, a near-α Ti-alloy, finds use in aeroengines due to its favorable properties. However, the alloy exhibits Dynamic Strain Aging (DSA) in the temperature range of 375-475 °C, that can cause it to fail early during service. As DSA is due to the micro-scale interaction between the diffusing solutes and mobile dislocations, a crystal plasticity model is developed in this work to capture this phenomenon. Additionally, the influence of the α (HCP) and β (BCC) laths of the transformed-β colony of this alloy on the DSA behavior is captured by using an equivalent model based on Taylor’s assumption. The effect of slip system dependent lath and colony size effect due to Burger’s Orientation Relation is also incorporated. Crystal plasticity finite element method simulations of polycrystalline domains, representative of Timetal-834, are performed for calibration and validation of the model using the available temperature dependent experimental data, and successfully capture the flow stress and DSA behavior. The strain rate dependency of DSA predicted by the model also shows an excellent agreement when compared with experimental data. Microstructural analysis of the simulations show that the orientation of grains/colonies have a strong influence on the aging time and hence the DSA response. Also, the initiation of DSA and frequency of serrated slip on the aligned systems of laths show differences due to dissimilar resistances and constraints on plastic flow. Overall, the model developed in this work can capture the microstructure dependent DSA and can be utilized for engineering of Timetal-834.

Numerical and experimental study of the size effect on deformation behavior and quality of microembossed multi-channel structures

With an uptrend of product miniaturization and precision manufacturing, the microembossing process of sheet metal has been widely used, and the corresponding researches have been conducted from the aspects of both experimental and theoretical explorations. Many unknowns, however, remain, such as size effect and it-induced scatters of deformation behaviors and product qualities. In this research, the multi-channel structures with various thicknesses made by a microembossing system using pure copper sheets were employed as case studies. The crystal plasticity finite element method simulations and experiments were conducted to study the effects of grain size and sheet thickness on the process and product of microembossing in terms of load-stroke relation, dimensional accuracy, and surface quality. From both the experimental and numerical results, it is revealed that the grain size effect causes deviated load and non-uniformity in deformation. The dimensional accuracy designated by the variations in thickness and height is affected by both grain size and sheet thickness. As grain size increases, the thickness reduction becomes more dramatic, and the thinnest location is at the corner zone. The height of the channel bottom increases with grain size, while the peak height fluctuation due to grain size is relatively minor. In addition, various surface defects on the surface of the embossed multi-channel structure were observed, including microvoids and micro scratches on the sidewalls, and wrinkles and grooves on the peak and bottom surfaces. From the inner to outer of the structures, microvoids gradually change to micro scratches, which become denser and longer as grain size increases in 100 μm thick copper sheets and also more severe with the increasing sheet thickness. All of these enrich the understanding of sheet metal microembossing and facilitate design solution generation in the optimization of the microembossing process and the quality of the embossed structures.

Simulated effects of sample size and grain neighborhood on the modeling of extreme value fatigue response

Assessing the size of representative volume elements (RVEs) for fatigue-related applications is challenging. A RVE relevant to random microstructure requires a volume of material that is sufficiently large to capture the grain/phase heterogeneity that captures all statistical moments of the distribution of the driving force for fatigue crack formation at “hot spot” grains. Consequently, the large size of a microstructure RVE required to study fatigue phenomena is largely computationally intractable and difficult to explore. A more realistic objective in this work is to systematically study, as a function of the size of a statistical sample of microstructure, trends towards convergence of the simulated distribution of driving force for fatigue crack formation. The present work accordingly leverages the recently developed open-source PRISMS-Fatigue framework [Yaghoobi et al., npj Comput. Mater., 7, 38 (2021)] to examine the trends in convergence of extreme value distributions (EVD) of Fatigue Indicator Parameters (FIPs) in progressively larger polycrystalline microstructure realizations of FCC Al alloy 7075-T6 using crystal plasticity finite element method simulations. The results are compared to the traditional method in which ensembles of statistical volume elements (SVEs) are simulated to build up statistics intended to approximate those associated with a larger volume of material. The convergence of EVDs with increase of size of a SVE of microstructure is closely related to the extent of grain nearest neighbor (NN) interactions. Accordingly, the sensitivity of the local micromechanical response at hot spot grains is quantitatively investigated by systematically varying the orientations of NN grains. Results indicate that SVEs with cubic crystallographic texture tend towards convergence of the EVD of FIPs with tens of thousands of grains while the random and rolled textures require larger volumes. Simple relationships based on microstructure parameters (e.g., Schmid Factor, grain size, NN misorientation) do not completely correlate to fatigue hot spot grains. Finally, the sensitivity of the extreme value fatigue response at hot spot grains extends to the 3rd NN when a single neighborhood grain orientation is altered.

Characterization of size-affected non-uniform deformation of polycrystalline copper

In polycrystalline materials, with the increase in grain size relative to the macrostructure, the collective behavior of crystal grains affects their macroscopic deformation field. To investigate the effect of relative size on the mechanical behavior of polycrystalline materials, the interaction between the microstructure-induced non-uniform deformation and the specimen shape-induced non-uniform deformation was evaluated based on experimental and numerical studies of uniaxial tensile tests of polycrystalline copper specimens with a curved gauge section. The effects of the macroscopic stress gradient and grain size on the strain field of the specimen were evaluated using specimens with different curvature radii obtained from different thermal treatment conditions. The development of strain distribution was measured using the digital image correlation method. A high strain concentration was observed at the minimum cross-section region in the specimen with smaller grains, whereas such strain concentration was relaxed in the specimen with larger grains because a random strain distribution occurred owing to the polycrystalline structure. A full-scale crystalline plasticity finite element method simulation, under conditions similar to those in the experiment, was then performed. Deformation concentrated zone, in which the length and width depended on the grain size, occurred in the polycrystalline specimen. The cross-section of the specimen was locally reduced when the deformation concentrated zone reached the free surface, and the tensile force became smaller for the specimen with larger grains. To discuss the relative specimen size effect, the plastic strain was divided into local and nonlocal plastic strains. Both the experimental and simulation results clarified that the nonlocal plastic strain gradient evaluated in the finite volume region increased with the region-averaged stress. From these results, we proposed a constitutive equation for the plastic strain as a function of local stress and finite volume averaged stress. The nonlocal plastic work for the evaluation region, which is estimated using the nonlocal strain gradient, increased with the stress during the strain-hardening stage in both the simulation and experimental results.

Crystal plasticity modeling of a titanium alloy under thermo-mechanical fatigue

A crystal plasticity model is developed to understand the fatigue behavior of Ti-6Al-4V under in-phase (IP) and out-of-phase (OP) thermo-mechanical loading. A systematic calibration and validation strategy using experimental data of isothermal monotonic and fatigue is developed to parameterize the model. Subsequently, crystal plasticity finite element method simulations under IP and OP thermo-mechanical fatigue loads are performed. A comparison of the stress range and hysteresis with cycles, between the IP and OP cases, shows that the proposed model is able to capture their differences appropriately. The stress distribution in the microstructure also clearly explains the larger life under IP as compared to OP as observed in experiments.

Dislocation density informed eigenstrain based reduced order homogenization modeling: verification and application on a titanium alloy structure subjected to cyclic loading

This manuscript presents a dislocation density informed eigenstrain based reduced order homogenization model (DD-EHM), and its application on a titanium alloy structure subjected to cyclic loading. The eigenstrain based reduced order homogenization (EHM) approach has been extended to account for the presence of HCP (primary α phase) and BCC (β phase) grains, within which the deformation process is modeled using a dislocation density based crystal plasticity formulation. DD-EHM has been thoroughly verified to assess the accuracy of the reduced order model in capturing local and global behavior compared with direct crystal plasticity finite element method simulations. A structural scale study of titanium alloy Ti-6242S is performed using DD-EHM to quantify and characterize the spatial distribution and evolution of the dislocation pile-ups subjected to cyclic loading. The evolution of pileups at two spatial scales are tracked using a nonlocal parameter based on dislocation density discrepancy across neighboring grains. The effect of non-uniform texture on the response of the structural component has been investigated.

Crystal plasticity finite element method simulation for the nano-indentation of plasma-exposed tungsten

In this work, the nano-indentation of plasma-exposed tungsten is simulated at room temperature and elevated temperature (300–700 K) by the recently developed crystal plasticity finite element model. A nonlinear function is applied to characterize the depth profile of plasma-induced dislocation density in the sub-surface region. The model parameters are calibrated by comparing the simulated results with corresponding experimental data at 300 K for both the force-depth and hardness-depth relationships. Furthermore, the mechanical responses of plasma-exposed tungsten are predicted at 500 K and 700 K in order to characterize the plasma effect at the fusion-relevant operational temperature. The dominant results and conclusions are that: (1) The heterogeneously distributed dislocations in the sub-surface region induced by the plasma exposure are responsible for the increase of hardness at 300 K. (2) The plasma-induced microstructural modification does not yield to considerable increase of hardness at operational temperature. (3) The expansion of the plastic zone in the sub-surface region is, to some extent, limited by the presence of plasma-induced dislocations. Whereas, the increase of temperature can effectively reduce this limitation.

Grain Size Dependence of Uniform Elongation in Single-Phase FCC/BCC Metals

We studied the dependence of uniform elongation on grain size in the range of submicron to millimeter for single-phase FCC/BCC metals by reviewing recent experimental results and applying crystal plasticity finite element method simulation. In the order of increasing grain size, uniform elongation can be divided into three stages, namely low elongation stage, nearly constant elongation stage, and decreased elongation with large scatters stage. Low elongation stage features a dramatic increase near the critical grain size at the end of the stage, which is primarily attributed to the emergence of dislocation cell size transition from ultrafine to mid-size grain. Other factors can be neglected due to their negligible influence on overall variation trend. In nearly constant elongation stage, uniform elongation remains unchanged at a high level in general. As grain size keeps growing, uniform elongation starts decreasing and becomes scattered upon a certain grain size, indicating the initiation of decreased elongation with large scatters stage. It is shown that the increase is not linear or smooth but rather sharp at the end of low elongation stage, leading to a wider range in nearly constant elongation stage. The grain size dependence of uniform elongation can serve as a guiding principle for designing small uniaxial tensile specimens for mechanical testing, where size effect matters in most cases.

On the mechanism of asymmetric ductile–brittle transition in microcutting of (111) CaF2 single crystals

In contrast to forming an amorphous deformed layer, lattice rotation induced asymmetric ductile–brittle transition (aDBT) is first identified in the microcutting of (111) CaF2 single crystals through a systematic experimental study of the machined surface profile, cutting force, crack morphology, and material microstructural changes. Crystal plasticity finite element method simulation has been developed to elucidate the underlying mechanism of variation in macroscopic cutting forces, meso-scale dislocation activities, and lattice rotation under the microcutting induced stress field. The characterised aDBT evokes a reflection on determining the critical chip thickness which plays an essential role in ductile-regime microcutting of brittle materials.

Modeling the Hall-Petch Relation of Ni-Base Polycrystalline Superalloys Using Strain-Gradient Crystal Plasticity Finite Element Method

Abstract A strain-gradient crystal plasticity constitutive model was developed in order to predict the Hall-Petch behavior ofa Ni-base polycrystalline superalloy. The constitutive model involves statistically stored dislocation and geometrically necessarydislocation densities, which were incorporated into the Bailey-Hirsch type flow stress equation with six strength interactioncoefficients. A strain-gradient term (called slip-system lattice incompatibility) developed by Acharya was used to calculate thegeometrically necessary dislocation density. The description of Kocks-Argon-Ashby type thermally activated strain rate was alsoused to represent the shear rate of an individual slip system. The constitutive model was implemented in a user materialsubroutine for crystal plasticity finite element method simulations. The grain size dependence of the flow stress (viz., the Hall-Petch behavior) was predicted for a Ni-base polycrystalline superalloy NIMONIC PE16. Simulation results showed that thepresent constitutive model fairly reasonably predicts 0.2 %-offset yield stresses in a limited range of the grain size.Key wordscrystal plasticity, strain gradient plasticity, finite element method, hall-petch relation, polycrystal.

A methodology to study crystal plasticity inside a compression test sample based on image correlation and EBSD

Modified compression tests in a coarse-grained austenitic stainless steel have been carried out in order to examine the crystal plasticity behavior for large plastic deformations. The measurements of local in-plane strains provide deeper insight into the deformation process on the local scale. These measurements are performed by digital image correlation technique (DIC) in combination with local crystal orientation measurements by using the electron backscatter diffraction technique (EBSD). Split test samples are prepared to track the strong microstructural changes during deformation, which is done incrementally in 10% steps up to 60% total macroscopic strain. The clear correlation of local strains with crystal orientation changes – e.g. in the case of mechanical twinning – permits to identify the acting deformation mechanisms. Such, experimentally determined local strain maps can be used for verification of crystal plasticity finite element method simulations (CPFEM).