Anisotropic Plastic Deformation Research Articles

A reduced Yld2004 function for modeling of anisotropic plastic deformation of metals under triaxial loading

Solid elements are increasingly utilized in finite element analysis of sheet metal stamping processes with the rising application of advanced high strength steels (AHSSs) and aluminum alloys in auto industries as these advanced materials fail in a form of rupture with negligible necking during sheet metal stamping. However, there are rare orthotropic yield functions for the description of directional dependence of plastic deformation of body-centered cubic (BCC) materials and face-centered cubic (FCC) metals under spatial loading, especially for metals with moderate anisotropy. For this purpose, the Yld2004-18p function is revisited and modified to provide satisfactory predictability of orthotropic behavior of BCC and FCC materials under spatial loading with reduced experimental costs for the calibration of orthotropic coefficients. The reduced Yld2004 equation is utilized to characterize the directional dependence of plastic behavior of AHSSs and aluminum alloys to verify its promising accuracy and cost efficiency. The reduced Yld2004 function is also implemented into finite element analysis to assess its accuracy and computation efficiency compared with the Hill48, Yld2004-18p and the anisotropic Drucker equations. The application in both analytical prediction and numerical analysis proves that the reduced Yld2004 function provides competitive predictability of anisotropic plastic deformation for BCC and FCC metals with moderate directionality under triaxial stress states, but the cost for the parameter calibration is cut down by about half compared to the Yld2004-18p function. Considering the satisfactory accuracy, reduced cost for the parameter calibration as well as the fact that most metals are of gentle dependence on loading direction, the reduced Yld2004 function is expected to reliably reproduce actual stamping processes of the majority of AHSSs and aluminum alloys with virtual models thereby improving the credibility of both numerical design of tools and process optimization.

Crystal plasticity analysis of cylindrical holes and their effects on the deformation behavior of Ni-based single-crystal superalloys with different secondary orientations

The effects of cylindrical holes and secondary orientations on the deformation behavior of Ni-based single crystals were investigated by in-situ tensile experiments and crystal plasticity simulations using models based on dislocation density evolution. In the experiments and simulation, a load was applied along [001] (primary orientation), while the holes were prepared along two different secondary orientations: [100] (orientation A) and [110] (orientation B). We obtain excellent agreement between simulation and experiments and reveal that the addition of hole induces multi-axil stress condition in the single crystal sample, which facilitates the plastic deformation and promotes anisotropic plastic deformation around hole. For specimen with three holes, the interaction among the holes induces plastic slip in some areas, which enhances the plastic slip in the regions adjacent to the side holes and inhibits the plastic slip in the regions around central hole. Therefore, the plastic deformation around the side hole demonstrates unsymmetrical features, and the plastic deformation around the side hole is larger than that around the central hole, which preferentially induces cracks. The secondary orientations influence the activities of the slip systems. Compared to the specimens with orientation B, more slip systems are activated and the plastic slips are homogeneous for specimens with orientation A; therefore, the fracture strains and tensile strengths of the specimens with orientation A are higher than those of the specimens with orientation B.

Deformation behaviour of small scale cp‐titanium specimen with large grains

AbstractTo describe the material behaviour of the microstructure of commercially pure (cp‐) titanium with the Finite Element (FE) Method, a crystal plastic material model is used. The anisotropic plastic deformation is considered by specifying the slip systems of the hexagonal‐closed‐packed (hcp) crystal structure. To circumvent the difficulties associated with possible non‐uniqueness of the set of active slip systems, a rate‐dependent formulation is used. Because of the volume preserving plastic deformation, locking effects can arise, which are dealt with by a modified F‐bar deformation gradient. To investigate the material behaviour of cp‐titanium small scale tensile test simulations are performed. Electronic backscatter diffraction (EBSD) investigations of the sample provides the specific grain orientations of the microstructure to perform realistic simulations.

Anisotropic plastic deformation of single crystals of the MAX phase compound Ti3SiC2 investigated by micropillar compression

The anisotropic deformation behavior of single crystals of Ti3SiC2 has been investigated at room temperature as a function of loading axis orientation and specimen size by micropillar compression tests. Basal slip is found to be only the operative slip system at room temperature. The a/3[12¯10] basal dislocation responsible for basal slip dissociates into two partial dislocations of the Shockley-type and glides between Ti1 and Si atomic layers, as confirmed both experimentally and theoretically. The CRSS value for basal slip increases with the decrease in the specimen size, following an inverse power-law relationship with a very large power-law exponent of about 1.0, which is almost the upper limit of those reported for FCC metals. When the loading axis is parallel to the basal plane, kink band formation occurs only after the occurrence of basal-plane delamination and the subsequent activation of a-dislocations gliding on the basal plane. Kink bands consists of a/3[12¯10] basal edge dislocations of the same sign, each of which had glided between Ti1 and Si atomic layers. These results indicates that the kink formation can simply be interpreted by the classical dislocation-based kink-formation model.

Measurement of Differential Hardening under Biaxial Stress of Pure Titanium Sheet

Biaxial stress tests of a commercially pure titanium sheet (JIS #1) using the cruciform specimen and the servo-controlled biaxial testing machine have been carried out in order to elucidate its anisotropic plastic deformation behavior. The geometry of the cruciform specimen is identical to that regulated by the ISO 16842. Nine linear stress paths, σx (rolling direction): σy (transverse direction) = 1:0, 4:1, 2:1, 4:3, 1:1, 3:4, 1:2, 1:4, and 0:1 in the first quadrant of the principal stress space are applied to the cruciform specimens. Contours of plastic work in the principal stress space and the directions of plastic strain rates at selected levels of plastic work have been precisely measured. The range of the equivalent plastic strain applied to the specimens is 0.002 ≤ ≤ 0.01. The shapes of the work contours significantly change with increasing the test material exhibits differential hardening (DH). Using the data of the work contours and the directions of plastic strain rates, the applicability of selected anisotropic yield functions to the accurate prediction of the plastic deformation behavior of the test material is examined.

Modeling the anisotropy of hot plastic deformation of two-phase titanium alloys with a colony microstructure

Two-phase titanium alloys deform heterogeneously in primary hot working due to the strong anisotropy of plastic deformation of colony structure associated with the transformation crystal structure, morphology and orientation relationship between the constituent phases. To understand the heterogeneous deformation in primary hot working, a homogenized crystal plasticity constitutive model is developed for a single colony which relates anisotropic deformation behavior to microstructural features. Efforts are made to model the morphological effects which cause the abnormally low measured critical resolved shear stress (CRSS) of two basal <a> slip systems and the anisotropic Hall-Petch strengthening associated with the Burgers orientation relationship. The model is able to capture the deformation characteristics and texture evolution in compression of colony structure. It is found that the morphological effects cause the formation of transverse texture and continuous flow softening in hot compression.

Experimental and Numerical Study of Texture Evolution and Anisotropic Plastic Deformation of Pure Magnesium under Various Strain Paths

The deformation behavior and texture evolution of pure magnesium were investigated during plane strain compression, simple compression, and uniaxial tension at room temperature. The distinctive stages in the measured anisotropic stress‐strain responses and numerically computed strain‐hardening rates were correlated with texture and deformation mechanisms. More specifically, in plane strain compression and simple compression, the onset of tensile twins and the accompanying texture‐hardening effect were associated with the initial high strain‐hardening rates observed in specimens loaded in directions perpendicular to the crystallographic c‐axis in most of the grains. The subsequent drop in strain‐hardening rates in these samples was correlated with the exhaustion of tensile twins and the activation of pyramidal &lt;c+a&gt; slip systems. The falling strain‐hardening rates were observed in simple compression and plane strain compression with loading directions parallel to the c‐axis where the second pyramidal &lt;c+a&gt; slip systems were the only slip families that can accommodate deformation. For uniaxial tension with the basal plane parallel to the tensile axis, the prismatic &lt;a&gt; and second pyramidal &lt;c+a&gt; slips are the main deformation mechanisms. The predicted relative slip and twin activities from the crystal plasticity simulations clearly showed the effect of texture on the type of activated deformation mechanisms.

Study of Anisotropic Plastic Behavior in High Pressure Torsion of Aluminum Single Crystal by Crystal Plasticity Finite Element Method

In this study, a crystal plasticity finite element method (CPFEM) model has been developed to investigate the anisotropic plastic behavior of (001) aluminum single crystal during high-pressure torsion (HPT). The distributions of equivalent plastic strain and Mises stress recorded on the sample surface are presented. The directional variations of plastic strain and Mises stress with the development of four-fold symmetry pattern are observed along the sample circumference. The crystallographic orientation evolution along the tangential direction is studied, and the corresponding lattice rotation and slip trace are predicted, respectively. The plastic anisotropy mechanism is discussed in detail based on the theory of crystal plasticity. The simulation results reveal that the differences in slip systems activation (dominant slip and multiple slips) are responsible for the anisotropic plastic deformation in HPT.

Anisotropic yield function based on stress invariants for BCC and FCC metals and its extension to ductile fracture criterion

It is essential to accurately model the anisotropic plastic deformation and ductile fracture of metals in order to guarantee the reliable numerical analysis and optimization of metal forming. For this purpose, the Drucker function is revisited. Effect of the third stress invariant in the Drucker function is analyzed and calibrated for metals with body-centered cubic (BCC) and face-centered cubic (FCC) crystal systems based on the yielding and plastic flow of both crystal plasticity and biaxial tensile experiments. The calibrated Drucker function is extended into an anisotropic form using a fourth order linear transformation tensor. The anisotropic flexibility is enhanced by two approaches: non-associate flow rule (non-AFR) and the sum of n-components of the anisotropic Drucker function. The proposed anisotropic Drucker function is applied to model the anisotropic behavior of both BCC and FCC metals. The predicted anisotropic behavior is compared with experimental results. The comparison demonstrates that the anisotropy is accurately modeled for both BCC and FCC metals by the anisotropic Drucker function. The anisotropic Drucker function is also implemented into numerical analysis of tension of specimens with a central hole to investigate its computation efficiency under spatial loading compared with the Yld2000-18p function. It is found that the proposed anisotropic Drucker function can reduce about 60% of computation time in case that the Yld2000-18p function is substituted by the anisotropic Drucker function in numerical computation due to its simplicity compared to the Yld2000-18p function. A ductile fracture criterion is also developed by coupling the Drucker function with the first stress invariant. The modified Drucker function is reformulated to investigate the effect of the stress triaxiality and the normalized third invariant on ductile fracture. Comparison of the modified Drucker fracture locus with the experimental results of AA2024-T351 demonstrates that the modified Drucker criterion accurately illustrates the fracture stress of the alloy in wide stress states with the stress triaxiality ranging from −0.5 in plane strain compression to 0.6 in tension of notched specimens. The modified Drucker fracture criterion is expected to be less sensitive to the change of strain path considering that the criterion describes fracture in the stress space. Accordingly, the anisotropic Drucker yield function and the pressure-coupled Drucker fracture criterion are suggested to model anisotropic plastic deformation and to predict the onset of failure for both BCC and FCC metals due to simple implementation in numerical analysis under spatial loading and computation efficiency with brick elements.

Origin of the Bauschinger effect in a polycrystalline material

There is a long and lively debate in the literature about the origin of the Bauschinger effect in polycrystalline materials, the most widely accepted explanation being the easier movement of dislocations during reverse loading causing the reduction of the yield stress. Other explanations include incompatible deformation at the grain scale and change of dislocation cell structures during forward and reverse loading, but recent publications show these phenomenological explanations of the Bauschinger effect are not holistic. In the experimental work presented here, we have investigated the role of micro residual lattice strain on the origin of the Bauschinger effect in type 316H austenitic stainless steel using in-situ neutron diffraction. Standard cylindrical specimens were tension-compression load cycled at room temperature with the loading interrupted at incrementally larger compressive and tensile strains followed by reloading to the tensile loop peak strain. Mirror symmetric cyclic tests were also performed with tensile and compressive load interruptions followed by compressive reloading to the compressive loop peak strain. A strong correlation is demonstrated between the evolution of residual lattice strain in the grain families and the change in magnitude in macroscopic yield stress, peak stress and the shape of the yielding part of the stress-strain curve for both the cyclic tension yield and compression yield tests. This implies that the residual lattice strain generated by grain scale elastic and plastic deformation anisotropy is the primary source of the Bauschinger kinematic hardening effect observed in type 316H austenitic stainless steel.

An anisotropic elastoplastic damage constitutive model for 3D needled C/C-SiC composites

This paper established a combined elastoplastic damage model to analyze the nonlinear mechanical behavior of 3D needled C/C-SiC composites. Inelastic deformation and stiffness degradation of the composite were characterized by the plasticity and damage theories. An innovative plastic potential function containing variable parameters was proposed to consider particularly the anisotropy of plastic deformation in each material direction. Based on the Weibull statistical distribution of the material strength, an exponential damage state function was established to characterize stiffness degradation for the composite in each material direction. Parameters of this constitutive model were determined from experiments data. It can be found that the nonlinear stress-strain curves for the composite under off-axis tensile and shear loadings can be accurately described by the model. The yield and damage surfaces of the composite were also studied. Finally, the constitutive model was validated by analyzing the mechanical behavior of a composite plate containing a center-hole subjected to tensile load.

Material modeling of 6016-O and 6016-T4 aluminum alloy sheets and application to hole expansion forming simulation

This study investigates the influence of heat treatment on the anisotropic plastic deformation behaviors of 6016-O and 6016-T4 aluminum alloy sheets. The two material samples were fabricated from the same lot and, therefore, have the same grain size and crystallographic texture. Biaxial tensile tests using both cruciform and tubular specimens are performed for many proportional stress paths in the first quadrant of stress space. The test results reveal that the degree of differential hardening (DH) is much larger in 6016-T4 than in 6016-O. It is shown that the work contour shape of 6016-O is controlled by crystallographic texture, whereas that of 6016-T4 presumably depends on GP-zones as well. From the biaxial stress test data, an appropriate yield function for each material is determined and employed in the finite element analysis of the hole expansion forming process. It was found that the Yld2000-2d yield function provides proper material representations of the plastic behavior of both material samples in the sense that it correctly predicts the fracture or localized neck locations, which occurs in the hole edge vicinity. For 6016-O, the thickness strain profile predicted with the Yld2000-2d yield function, which accounts for the DH of the material, is in better agreement with the experimental results than that obtained with the isotropic hardening model. For 6016-T4, the Yld2000-2d yield function with an exponent of 8 with the isotropic hardening assumption leads to a fair prediction of the experimental data. In order to enhance the accuracy of forming simulations for 6016-T4, it is necessary to develop a material model that is capable of reproducing the significant DH resulting from the GP-zones.

Real-Time Observations of Electrochemical Reactions in Rechargeable Energy Storage Systems

Electrodes in rechargeable batteries undergo complex electrochemically-driven phase transformations upon driving Li ions into their structure. Such phase transitions in turn affect the reversibility and stability of the battery. This presentation gives an overview of the PI’s research program on in-situ transmission electron microscopy (TEM) of battery materials. In-situ TEM has been shown to be a very powerful technique in shedding light to some of the mysteries in electrochemical performance of new materials. Various anode materials including SnO2, MnO2, ZnSb were subjected to lithiation process and the transport of Li ions was visualized within their atomic structure. For SnO2 nanowires, it was observed that the Li ion transport results in local strain development preferably along (200) or (020) plans and [001] crystallographic directions. The lithiation behavior in the presence of twin boundary defects was completely different compared to pristine state with no twin boundary defect. We showed that twin boundaries in general provide a more accessible pathway for Li ion transport. Anisotropic plastic deformation was also observed along [010] directions of MnO2 nanowires. Sb-based intermetallics, such as Zn-Sb system, which have been proved to be promising anode materials for Li-ion batteries, are also capable of storing of sodium ions. We investigated the microstructural changes and phase evolution of the Zn-Sb intermetallic nanowires using in-situ TEM. Zn-Sb alloys also exhibit a new cubic alloying phase Li2ZnSb that form by intermixing of the ABAB atomic ordering in hexagonal LiZnSb due to Li inclusion in their lattices. Our results indicate that the reaction between Zn-Sb and sodium proceeds through a different pathway during the first compared to the subsequent cycles. Atomic resolution imaging shows that NaZnSb has a layered structure, which provides channels for fast Na+ diffusion.

Unusual plastic deformation and damage features in titanium: Experimental tests and constitutive modeling

In this paper, we present an experimental study on plastic deformation and damage of polycrystalline pure HCP Ti, as well as modeling of the observed behavior. Mechanical characterization data were conducted, which indicate that the material is orthotropic and displays tension-compression asymmetry. The ex-situ and in-situ X-ray tomography measurements conducted reveal that damage distribution and evolution in this HCP Ti material is markedly different than in a typical FCC material such as copper. Stewart and Cazacu (2011) anisotropic elastic/plastic damage model is used to describe the behavior. All the parameters involved in this model have a clear physical significance, being related to plastic properties, and are determined from very few simple mechanical tests. It is shown that this model predicts correctly the anisotropy in plastic deformation, and its strong influence on damage distribution and damage accumulation. Specifically, for a smooth axisymmetric specimen subject to uniaxial tension, damage initiates at the center of the specimen, and is diffuse; the level of damage close to failure being very low. On the other hand, for a notched specimen subject to the same loading the model predicts that damage initiates at the outer surface of the specimen, and further grows from the outer surface to the center of the specimen, which corroborates with the in-situ tomography data.

Nanoindentation induced deformation anisotropy in β-Si3N4 ceramic crystals

The influence of crystal orientation on nanohardness and indentation modulus of grains in polycrystalline β-Si3N4 was studied under nanoindentation at room temperature. The orientation of the individual grains was determined by electron backscatter diffraction (EBSD) prior to the indentation. Significant elastic and plastic deformation anisotropy was revealed. The elastic modulus exhibited a decrease for grains oriented from the basal towards the prismatic facets while the nanohardness values showed reversed tendency. The orientation dependence of indentation modulus was predicted by the Vlassak-Nix model and finite element model (FEM) calculations based on the elastic constants of β-Si3N4 single crystal and compared to the experimental results. A theoretical model was proposed to describe the nanohardness anisotropy on the basis of the possible slip systems of β-Si3N4. The calculations for elastic and plastic anisotropy are in good agreement with the experimental results.

A smoothing technique based beta finite element method (βFEM) for crystal plasticity modeling

This paper presents a novel class of smoothing techniques based beta finite element method (βFEM) for modeling of crystalline materials. The method is first examined by a simple standard patch test and applied in elastic problems. It is then implemented to model the anisotropic plastic deformation of rate-independent single crystals and bi-crystal. Several representative examples are studied to demonstrate the capability of proposed method with the integration algorithm for capturing the strain localization and dealing with plastic incompressibility. It is also performed to simulate the mechanical behavior of polycrystalline aggregates through modeling the synthetic microstructure constructed by Voronoi tessellation technique.

Identification of post-necking stress–strain curve for sheet metals by inverse method

Simulation of sheet metal forming requires the flow curve (i.e. the true stress–strain relation) over large strains. This paper presents a method for obtaining the flow curve of sheet metals over a large range of strain through the combination of simple tensile test and finite element analyses. The appropriate finite element model for accurate simulation of the anisotropic plastic deformation during diffuse necking was determined. Different hardening functions were evaluated for their capabilities in approximating the entire flow stress curves up to localized necking. A modified Hockett–Sherby function was proposed and its performance was demonstrated.

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.

Mechanistic Understanding of Li Transport in Rechargeable Batteries

Electrodes in rechargeable batteries undergo complex electrochemically-driven phase transformations upon driving Li ions into their structure. Such phase transitions in turn affect the reversibility and stability of the battery. It is of prime importance to better understand how Li ions transport within the host electrodes and what phase transitions are triggered during such interaction. This presentation gives an overview of the PI’s research program on in situ transmission electron microscopy (TEM) of battery materials. Various anode materials including SnO2, Zn-Sb were subjected to lithiation process and the transport of Li ions was visualized within their atomic structure. For SnO2 nanowires, it was observed that the Li ion transport results in local strain development preferably along (200) or (020) plans and [001] crystallographic directions. Anisotropic plastic deformation was also observed along [010] directions of MnO2 nanowires. Zn-Sb alloys also exhibit a new cubic alloying phase Li2ZnSb that form by intermixing of the ABAB atomic ordering in hexagonal LiZnSb due to Li inclusion in their lattices.

Cold Formability of Automotive Sheet Metals: Anisotropy, Localization, Damage and Ductile Fracture

Experimental and numerical investigations on the characterization and prediction of cold formability of two different types of automotive steel sheets, a ferritic stainless steel sheet (AISI 439) and a dual-phase steel sheet (DP600) are performed in this study. Due to the different microstructure configurations, these two steels show significant differences in plasticity behavior as well as failure mechanisms. The ferritic stainless steel shows strong anisotropic plastic deformation in terms of both yielding and hardening, whereas the dual-phase steel behaves quite isotropic resulting from the mixture of two phases. However, unlike the localization dominant failure mechanism of the ferritic stainless steel, the incompatible deformation due to the distinctions of the mechanical properties of two phases naturally results in early damage and extensive damage development prior to localization, or ductile fracture without localization. In this study, all these features are taken into account for an accurate prediction of formability. A general modelling framework with specifications for these separate features is formulated and applied to the two steels.