Equivalent Plastic Strain Research Articles

Effects of T1/T2 precipitates on deformation behavior and microstructure evolution of AA2099 Al–Li alloy: experimental investigation and crystal plasticity finite element modeling

In the present study, effects of T1/T2 precipitates on microstructure characteristics and texture evolution of various AA2099 Al–Li alloy (AA2099-A and AA2099-B) samples are systematically investigated by conducting uniaxial compression experiments at room temperature, followed by electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM) measurements as well as crystal plasticity finite element (CPFE) simulation. The heat treatment for AA2099-A sample consists of solution treatment at 540 °C/1 h and artificial aging at 250 °C/1 h followed by water quenching, while the heat treatment for AA2099-B sample includes solution treatment at 540 °C/1 h and artificial aging at 250 °C/24 h followed by water quenching. Experimental results demonstrate that although dynamic recovery (DRV) serves as the major restoration mechanism for both samples, AA2099-A sample with T1 phase possesses obviously higher mechanical response by comparison with AA2099-B sample with T1/T2 phase. This observation shows a strong precipitate hardening effect derived from these dense and large-sized T1 precipitates in AA2099-A sample. Numerical results based on CPFE simulation demonstrate the occurrence of inhomogeneous plastic strain within the constructed grain-based representative volume element (RVE) model during uniaxial compression. Further statistical analysis on the coefficient variant about equivalent plastic strain verifies this issue and demonstrates that plastic strain distributes more homogeneously in AA2099-A sample than in AA2099-B sample. These dense and large-sized T1 precipitates are responsible for this phenomenon and they result in the fast rotation of grain orientation from <111>//ED to <110>//ED during uniaxial compression.

Numerical and Experimental Studies on Hydro-Forming of a Thin Metallic Disc

This paper deals with the hydro-forming of a flat thin metallic disc to achieve a forward domed disc which will be subsequently adopted to manufacture a rupture disc. The plastic deformation induced by the hydraulic energy is numerically simulated through an isotropic hardening plasticity model using a non-linear explicit finite element analysis (FEA). The variation in disc’s central deformation, thickness, equivalent plastic stress and equivalent plastic strain with respect to the applied hydraulic pressure are determined from FEA simulations. The hydro-forming setup is then designed and manufactured, and the metallic disc is experimented under hydro-forming process. The reduction in thickness due to stretching of the thin disc is evaluated from experiment and simulation and a close agreement is found. This research attempt helped in finalizing the hydro-forming fluid pressure, the feasibility and the accuracy of practically achieving the desired geometry of the metallic disc. The near-fixidity effects on abrupt variation in sheet thickness and plastic strain are well captured through simulations which are very difficult to be studied through hydro-forming experiments.

Numerical Constraints on Folding and Thrusting in Jiudong Basin: Implication for the Northeastward Growth of Qinghai–Tibetan Plateau

Under regional tectonic shortening in the northern margin of Qinghai–Tibetan Plateau, the fold-and-thrust belts composed of four thrust faults (North Qilian-Shan, North Yumu-Shan, South Heli-Shan, and North Jintanan-Shan) formed from southwest to northeast discontinuously sequentially in the Jiudong Basin area during Late Cenozoic. Meanwhile, the North Qilian-Shan, Yumu-Shan, and Heli-Shan ranges were formed successively, as the Earth's local surface was unequally uplifted. In this study, based on geological and geophysical observations, a simple two-dimensional elastic-plastic numerical finite element method model for a southwest-northeast section in Jiudong Basin is successfully established to simulate the spatiotemporal evolution of the local fold-and-thrust belts. Results show that the computed equivalent plastic strain concentration zones and the four observed thrust faults are consistently correlated in spatial position orientation and time sequence. The simulated upper-surface deformation is congruent with the observed topographic peaks and uplift sequences of the North Qilian-Shan, Yumu-Shan, and Heli-Shan ranges. This study provides a geodynamic basis for understanding the growth mechanism of the northern margin of Qinghai–Tibetan Plateau under tectonic horizontal shortening. Also, we provide a thorough sensitivity analysis for the model parameters of this particular geologic setting. Our sensitivity simulations, considering systematic case variations about the regional geometrical-material parameters, suggest the manifestation of three different possible evolution patterns of fold-and-thrust belts for a wedge above a decollement layer, with wedge plastic deformation migrating from 1) thick to thin end (well-known), 2) thin to thick end, and 3) both ends to middle. Finally, our results suggest that in this region, further growth of mountain ranges is expected to continue in the future.

Localizing Implicit Gradient Damage Based Treatment of Softening in Elasto-plasticity

As opposed to brittle fracture, the failure of ductile materials is preceded by severe plastic deformations. Microscopic mechanisms i.e., void growth and coalescence result in macroscopic property degradation causing softening, localization, and finally macroscopic crack. This contribution focuses on softening in elasto-plasticity and its mesh-objective description using an implicit gradient type of non-local damage mechanics framework. As reported in several studies Geers et al. (1998), Poh and Sun (2017), artificial widening of localization zone is observed when conventional implicit gradient type regularization is used. To circumvent this non-physical artifact, localizing implicit gradient damage (LIGD) formulation that is motivated by higher order continuum arguments, is adopted, Poh and Sun (2017). As opposed to previous remedies to artificial widening of the localization zone, LIGD proposes an internal length scale that decreases with deformation. A two-field (displacement-non-local equivalent plastic strain) hexahedra and a three-field (displacement-pressure-non-local equivalent plastic strain) tetrahedra element are formulated and implemented in commercial finite element software Abaqus through user element (UEL) subroutine. The effectiveness of the approach is demonstrated by solving two numerical examples.

Fracture behavior of prestressed ductile target subjected to high velocity impact - Numerical study

Impact studies are performed to evaluate the ballistic performance of material subjected to a high strain rate. At high velocities, the projectile penetrates through the material which leads to a fracture of the target body. The fracture behavior depends upon the condition of the target body. It is anticipated that the fracture behavior should depend upon the prestress condition of the target. Considering the aforementioned concern, the thermo-elastic-plastic finite element model is formulated using MSC Marc Mentat to analyze the effect of the prestress condition of the target body on fracture behavior. A detailed comparison has been presented considering four different prestress states subjected to impact by a blunt-shaped projectile. The continuum damage mechanics using a stress triaxiality-based damage model is used to simulate damage evolution and fracture. It is found that the presence of prestress alters the overall fracture response of the structure subjected to high strain rate deformation. In the presence of tensile prestress, the material resists the accumulation of damage which is due to the lower values of stress triaxiality and equivalent plastic strain. It is also found that the presence of tensile prestress inside the target body increases the ballistic performance, whereas the presence of compressive prestress inside the target body degrades the performance.

Numerical analysis of subgrain formation during metal cutting and rolling based on the crystal plasticity theory

The grain refinement technology is important in improving the metallic material properties without the requirement of additional alloy elements. Previously, we developed an efficient method for producing ultrafine-grained steel strips using a combination of cutting and heat treatment. However, the effect of cutting on recrystallization was not apparent. The objective of this study is to investigate the effects of metal cutting on static recrystallization and outline its advantages in grain refinement using numerical simulations based on the crystal plasticity theory. Simulation results show that shear deformation in metal cutting activates more slip systems than plane strain compression via rolling, even when considering the same equivalent plastic strain. The geometrically necessary dislocations are assumed to accumulate in the crystal because many slip systems are activated in shear deformation and improve grain refinement via static recrystallization in the subsequent heat treatment. This result indicates that the deformation type plays an important role in the recrystallization process. Thus, cutting is more efficient than rolling for the production of ultrafine-grained steel.

Inhomogeneous Deformation and Texture Evolution of 30SiMn2MoVA Steel Gun Barrel Processed by Radial Forging Based on Cross-scale Crystal Plasticity Finite Element Method

There is anisotropy in 30SiMn2MoVA steel gun barrel processed by radial forging which results in the low service life of the gun barrel. While the texture is the main reason for the anisotropy. The crystal plasticity finite element (CPFE) method is usually used to simulate the microstructure and the texture of the metal. In the present work, a two-dimensional polycrystalline finite element model based on electron back-scattered diffraction (EBSD) experiment data is developed to represent virtual grain structures of polycrystalline 30SiMn2MoVA steel. The displacement of nodes in the macro radial forging process finite element model is used as the cross-scale boundary condition in the CPFE model which realizes cross-scale simulation. The texture evolution and inhomogeneous deformation of 30SiMn2MoVA steel in the radial forging processing under three different forging ratios were simulated. The simulated texture results are consistent with the experimental results. The inhomogeneous deformation of grains is obvious and will intensify with the increase of the forging ratio. The distributions of stress and equivalent plastic strain in polycrystals are statistically Gaussian. With the increase of deformation, the further refinement of grains is due to the large shear strain in large grains.

拘束効果を考慮した極低サイクル疲労下におけるき裂進展条件クライテリオンの提案

The prediction of fracture behavior under extremely low cycle fatigue due to excessive loading is necessary for the life assessment of structures. ΔJ criterion has been used to assess the life under low cycle fatigue. However, the applicability of this method is not well confirmed under extremely low cycle fatigue. The reason is that fracture toughness is dependent on the loading conditions and geometry due to the constraint effect. In the previous study, the crack propagation criterion was proposed for a 1T-CT specimen of SUS316, focusing on the stress triaxiality and the equivalent plastic strain increment. However, no comparison has been performed for specimens of different shapes or materials, and more detailed verification is required. In this study, we performed generation phase and application phase analyses on 1.5T-CT and MT specimens. The results of both the generation and application phase simulation are in good agreement with the experimental results.

Investigation on surface integrity in laser-assisted machining of Inconel 718 based on in-situ observation

Inconel 718, a nickel-based superalloy, is widely used in the key parts of aero-engine owing to its high performance at elevated temperatures. Meanwhile, Inconel 718 is a typical difficult-to-cut material which is hard to obtain ideal surface integrity by conventional machining (CM). Laser-assisted machining (LAM) has a good potential to improve the machinability. In order to study the processing mechanism in the LAM of Inconel 718, the in-situ and ex-situ studies were presented in this paper. In the in-situ analysis, LAM and CM experiments were carried out based on in-situ observation and digital image correlation (DIC) technology. The Von Mises strain and equivalent plastic strain rate in the primary shear zone (PSZ) and cutting force were measured. According to the DIC results, under the experimental conditions of this paper, the average Von Mises strain and average equivalent plastic strain rate of PSZ in LAM increase by about 10% and 20% respectively due to the softening of Inconel 718 by laser heating, compared with CM. In-situ analysis shows that Inconel 718 in LAM is more prone to plastic flow, resulting in lower cutting forces. As for the ex-situ characterization, the surface roughness, residual stress and tool wear were measured. The measured results show that LAM can significantly reduce surface roughness and tool wear, and cause compressive residual stress on the machined surface.

The Effect of Tempering Duration on the Creep Behavior of the P91 Steels at 600℃

High performance martensitic heat resistant steels are widely used in fossil fuel power plant industry due to because of their good creep resistance at high temperatures. In-depth understanding of the high temperature inelastic deformation mechanism of such steels is crucial to ensure the reliable, safe and efficient operation of the power plant [1]. The martensitic steels have a complex microstructure with a hierarchical arrangement, including a collection of packets in the prior austenite grain, blocks in the packet and laths along with dispersed nanoscale strengthening phases (e.g., MX precipitates and carbides). The purpose of this paper is to study the creep mechanisms with regard to the microstructure of the P91 martensitic steel at high temperature by means of experimental characterisation and finite element simulation. In the present paper, the effect of tempering duration on the creep response of the P91 steel at 600 oC was experimentally examined with the precipitate size identified. Apart from the standard heat treatment (holding at 1060℃ for 40 min and then at 760℃ for 2 h) for the as-received P91 steels, secondary tempering treatment has been applied with different tempering time periods, e.g., 0 h (T0), 10 h (T10) and 20 h (T20) at 780℃. In order to simulate the creep response, crystal plasticity based micromechanical finite element model was developed based on the measured microstructure [2]. The crystallographic slip at the block level is accounted for using an exponential type of constitutive flow rule and the precipitate size effect is represented in the crystal plasticity model through the use of an internal variable in association with the slip resistance. The results show that the secondary tempering duration can significantly affect the creep behavior of the martensitic steel (see Fig. 1). It is found that with increasing tempering time period the precipitate size increases, which could lead to detrimental effect on material’s creep resistance. Similar effect of the precipitate size on the creep response has also been shown in literatures [3]. The measured creep response of the P91 steels with different heat treatments at different stress levels can be predicted by the developed micromechanical model. The micromechanical modelling results show (see Fig. 2) that the accumulated equivalent plastic strain during the creep is strongly heterogeneous and the levels of the strain localization depend on the tempering duration.

降伏曲面上に形成される尖り点を考慮した弾粘塑性モデルによるモードIき裂進展解析

It has been confirmed by experiments and crystal plasticity analysis that a vertex is formed at the loading point of the yield surface in the stress space during plastic deformation. However, most past deformation analyses for crack tip behavior have used plasticity models with a classical normality flow rule. In this study, we introduce a non-normality flow rule, which considers the formation of a vertex on the yield surface. We investigate the effect of vertex formation on Mode I crack growth behavior for cyclic loading. Numerical results show that both crack tip opening displacement and crack growth are greater for the model with the non-normality flow rule than for the standard normality flow rule. The distribution of equivalent plastic strain near the crack tip indicates that the model with the non-normality rule leads to localized plastic deformation, which is not seen in the case where the standard normality flow rule is adopted.

Constraint effect on fracture toughness resistance curves of an X60 pipe steel

The fracture toughness resistance curve (e.g. J-R curve and crack tip opening displacement (CTOD) or δ-R curve) is important in facilitating strain-based design and integrity assessment of oil and gas pipelines, where influence of ground movements and presence of planar weld flaws must be accounted for. In this paper, duplicate single edge bend (SE(B)) and clamped single edge tension (SE(T)) specimens with two different initial crack sizes were prepared from an X60 pipe steel. The longitudinally-oriented specimens were notched in the through-thickness direction and experimentally tested at room temperature. In general, the results showed the expected trends of higher resistance curves for both shallow-cracked versus deeply-cracked specimen types and tension versus bending loading modes. Eleven constraint parameters (i.e. QHRR, QSSY, QLM, QBM, A2, A2BM, h, Tz, Cp, Ap, Vp) were calculated based on three-dimensional (3-D) finite element analyses (FEA) for various tested SE(B) and SE(T) specimens.The results and analysis indicated that the shallow-cracked SE(B) specimens exhibited a constraint condition similar to the intrinsically low-constraint deeply-cracked SE(T) specimens. Among all of the constraint parameters, the Ap parameter based on the normalized equivalent plastic strain contour was found to have the most promising trend in terms of correlating the material’s toughness to constraint level for currently tested specimens. Further on-going investigations are underway to extend the evaluation to resistance curves for specimens made from X100, X80 and X70 pipe steels to allow for the characterization of strain hardening effect, as well as the evaluation of their associated weld metals and heat affected zones (HAZs).

Numerical and experimental performance evaluation of upgraded knee braces under cyclic load

In this paper, the seismic performance of the structure is analyzed by introducing a new angular knee element. Cyclic loads are applied to determine the seismic performance. The result is compared with a vertical knee element. The angular knee element showed better seismic performance as compared to the vertical knee element. The new short knee element studied in two positions including 1- a vertical knee element perpendicular to cross-brace is called VSKE 2- An angular knee element that is called ASKE. Using reduced knee section specimens for better performance. Effect of Angular knee element in knee-braced frames (KBFs) under Cyclic Loading was investigated by testing using a half scale specimen mounted on a reaction frame at two positions including horizontally for VSKE and inclined for ASKE. For experimental tests, specimens were loaded by using a hydraulic actuator. Finite element modelling was used for the simulation of detailed behavior using a verified experiment base model. It has been shown that the performance of knee element fuses can improve the ductile behavior of knee braced frames. Based on the results of vertical and angular cases, it has been shown that an increase of angle between main cross brace and short knee element (incline specimen) can reduce maximum equivalent plastic strain (EPEQ) in the web of knee element fuse.

A new model of critical resolved shear stress with the effect of geometrical relationship between slip plane and microstructure interface

A new model of critical resolved shear stress with the effect of geometrical relationship between slip plane and microstructure interface, was investigated using a crystal plasticity analysis with Cu polycrystals. The extended expression of the Bailey-Hirsch type model was used for the critical resolved shear stress. The effect of geometrical relationship between slip plane and microstructure interface was incorporated into the values for microstructural size parameter that express size effects in the extended expression of the Bailey-Hirsch type model l. The distribution of equivalent plastic strain and plastic shear strain on slip systems were investigated. At a nominal strain of 0.03, almost the same distributions of equivalent plastic strain were obtained with the simple grain size model and the new model where the effect of geometrical relationship between slip plane and microstructure interface were taken into account. On the other hand, the distributions of plastic shear strain on slip systems were different in the two models.

Plastic deformation behavior and constitutive modeling of Cu-50Ta alloy during hot compression

This paper presents a study on plastic deformation behavior of Cu–50Ta alloy at temperatures of 286–473 K and strain-rate of 0.01–6200 s−1. The effects of temperature, strain-rate, and strain on the yield strength, flow stress, and strain-rate sensitivity coefficient were determined. A phenomenological model was established to predict variation of the strain-rate sensitivity coefficient for Cu–50Ta alloy under dynamic compression. A Johnson–Cook constitutive model was established to predict the equivalent stress–equivalent plastic strain relationship under extreme deformation (high temperature and strain-rate). The results showed that the plastic deformation behavior of Cu–50Ta alloy was affected by temperature, strain-rate, and strain. The material exhibited obvious strain-rate strengthening and thermal softening. As the strain-rate increased, the yield strength logarithmically increased. At a temperature of 286 K, the strain-rate increased from 0.01 s−1 to 6200 s−1, and the yield strength increased from 543.75 MPa to 881.13 MPa. In addition, the yield strength linearly decreased as the deformation temperature increased. Under conditions of dynamic deformation, the variation of strain-rate sensitivity coefficient could be expressed as a function of strain-rate and strain. The phenomenological model accurately described the variation of the strain-rate sensitivity coefficient of Cu–50Ta under dynamic deformation conditions. The Johnson–Cook constitutive parameters, calibrated by experimental data, described the plastic deformation behavior of the alloy under high-velocity impact.

Experimental and numerical investigation of severe plastic deformation of copper sheets processed by modified-constrained studded pressing

In this study, mechanical behavior and microstructural evolution of copper sheets, produced by modified-constrained studded pressing (modified-CSP) as a severe plastic deformation (SPD) method, were investigated by experimental and numerical methods. A finite element model (FEM) was established to analyze distribution of equivalent total strain, distribution of equivalent plastic strain and residual stress for the complete first pass of the process. Local stress concentration was predicted by FEM. Also, copper sheets were deformed by the modified-CSP from the first to the tenth passes. The distribution of residual stress on the surface of the copper sheets was measured at each step of the process. Crack initiation and propagation were investigated by the non-destructive penetration test (PT). The residual stresses were predicted by X-ray diffraction (XRD) via sin2 Ψ method. The residual stresses were determined for the annealed and the first pass samples, +128.2 and +80.4 MPa, respectively. The maximum compression residual stress was −62.5 MPa for the tenth pass sample. The microstructural evolution including grain size and dislocation density of samples during the process were investigated by XRD pattern analysis. The average grain size had a significant decrease from ∼35 to ∼76 nm for annealed sample and tenth pass of modified-CSP, respectively.

極低サイクル疲労下における荷重条件を考慮したき裂進展条件式の評価

The validity of the crack propagation criterion under extremely low cycle fatigue due to earthquakes is still under discussed. Existing evaluation parameters are difficult to apply because they change under the constraint of restraining effects due to large plastic deformation. In a previous study, the crack propagation criterion was proposed and evaluated using equivalent plastic strain amplitude and stress triaxiality at the center of the plate thickness. Those parameters are physical quantities that are difficult to obtain from fracture experiments. In this study, the equivalent plastic strain amplitude and stress triaxiality at the crack front were analyzed under three different loading conditions to evaluate the applicable range in the direction of the plate thickness other than the center of the plate thickness and to improve the equation to be applicable near the plate thickness surface. As a result of the evaluation of the range of applicability in the thickness direction, it was found that the crack does not propagate near the surface in some cases.

On deformation characterisation of machined surfaces and machining-induced white layers in a milled titanium alloy

Machining-induced white layers and severely deformed layers are undesirable surface integrity features which can be formed when machining high-strength aerospace alloys. An orthogonal milling process has been designed and performed to assess the impact of cutting speeds, tool wear, cutting edge radius and climb vs conventional milling on white layer formation and plastic strain distribution. The plastic deformation in the machined surface associated with the formation of white layers in Ti-6Al-4V has been quantified using micro-grids of different length scales printed using the electron beam lithography technique. It was found that white layers formed via the severe plastic deformation mechanism, at equivalent plastic strain values in excess of 1.2 and in regions of the cutting arc with the instantaneous chip thickness of less than the cutting-edge radius and ploughing and rubbing being the dominant mechanisms. The results indicated that the magnitude of the measured strains and the depth of plastically deformed material was greater at lower cutting speeds, during climb milling and when machining with a larger cutting edge radius and tool flank wear land.

Spatiotemporal Evolution of Stress Field during Direct Laser Deposition of Multilayer Thin Wall of Ti-6Al-4V.

The present work seeks to extend the level of understanding of the stress field evolution during direct laser deposition (DLD) of a 3.2 mm thick multilayer wall of Ti-6Al-4V alloy by theoretical and experimental studies. The process conditions were close to the conditions used to produce large-sized structures by the DLD method, resulting in specimens having the same thermal history. A simulation procedure based on the implicit finite element method was developed for the theoretical study of the stress field evolution. The accuracy of the simulation was significantly improved by using experimentally obtained temperature-dependent mechanical properties of the DLD-processed Ti-6Al-4V alloy. The residual stress field in the buildup was experimentally measured by neutron diffraction. The stress-free lattice parameter, which is decisive for the measured stresses, was determined using both a plane stress approach and a force-momentum balance. The influence of the inhomogeneity of the residual stress field on the accuracy of the experimental measurement and the validation of the simulation procedure are analyzed and discussed. Based on the numerical results it was found that the non-uniformity of the through-thickness stress distribution reaches a maximum in the central cross-section, while at the buildup ends the stresses are distributed almost uniformly. The components of the principal stresses are tensile at the buildup ends near the substrate. Furthermore, the calculated equivalent plastic strain reaches 5.9% near the buildup end, where the deposited layers are completed, while the plastic strain is practically equal to the experimentally measured ductility of the DLD-processed alloy, which is 6.2%. The experimentally measured residual stresses obtained by the force-momentum balance and the plane stress approach differ slightly from each other.

Anisotropic hardening and evolution of r-values for sheet metal based on evolving non-associated Hill48 model

The uniaxial tensile tests and biaxial tensile tests were carried out to investigate the deformation behavior and yield loci of DC06 steel sheet. The continuous evolution of r-values was calculated by the proposed inverse method, which has higher accuracy and simpler form compared with the previous methods. Based on the equivalent plastic work principle, the anisotropic hardening, the evolution of r-values and subsequent yield loci were investigated. Then, an evolving non-associated Hill48 anisotropic plasticity model was formulated. Where, based on the constructed stress cost-function and constraint conditions of r-values, the anisotropic parameters coupling the distortional hardening and evolution of r-values were developed to characterize the anisotropy evolution. Moreover, the relationship between the uniaxial tensile plastic strain and the equivalent plastic strain was derived. Based on this, the continuous variation curves of anisotropic parameters with real equivalent plastic strain were obtained. The comparison between the experimental and prediction results indicates that the developed model can accurately capture the distortional hardening, evolution of r-values and yield loci simultaneously. Furthermore, the effect of distortional hardening and evolution of r-values on the subsequent yield surfaces and plastic potential is analyzed.