Plastic Instability Criterion Research Articles

Effect of grain size on the recrystallization kinetics and crystallographic texture of unidirectionally rolled Ti-15V-3Cr-3Al-3Sn alloy

In the present work, Ti-15V-3Cr-3Al-3Sn (Ti-15333) samples were solution annealed (SA) at two different temperatures (800 °C for 30 minutes and 1000 °C for 15 minutes) to investigate the effect of initial grain size (GS) on the cold rolling and recrystallization behavior. Average grain size (AGS) for samples SA at 800 °C and 1000 °C was 87±7.82 μm and 177±4.36 μm, respectively. Both the samples were cold rolled unidirectionally (UDR) upto 80 % thickness reduction, subsequently followed recrystallization at 780 °C. UDR samples showed elongated grain structure with a preferential formation of shear bands (SBs) in some grains. Formation of SBs was more prominent in coarse AGS sample and these bands were also found to be orientation sensitive. The frequency of occurrence of SBs was more in γ-fiber (ND//<111>) grains and Dillamore’s plastic instability criterion was used to explain their preferential occurrence in γ-fiber. Recrystallization was done at 780 °C, for various time periods ranging from 30 s to 30 minutes). 80 % UDR samples showed the formation of strong α- and γ-fibers in both the cases. Full recrystallization was attained within 10 minutes for the initial fine grained 80% UDR sample, and it exhibited a continuous γ-fiber texture. In contrast, initial coarse grained 80% UDR sample took 20 minutes to achieve complete recrystallization, and it showed a discontinuous γ-fiber texture. Notably, the {111}<112> texture component of the γ-fiber was prominently evident in both cases, while the α-fiber was entirely absent for both conditions.

Assessment of process-induced cracks in hot-working operations using crack susceptibility index based on plastic instability criteria

A processing map representing the efficiency of power dissipation as a function of the temperature and strain rate has been used as a guide to depict the hot workability of metallic alloys. However, it has limitations in indicating the local positions where process-induced cracks may occur during hot-working operations. A process-induced crack is formed during hot deformation because the plastic instability associated with crack formation is more favorable than normal flow under a given set of process conditions. This paper proposes a novel approach to assess local cracks using the crack susceptibility index (CSI), which is based on Ziegler's plastic instability criteria. This solution provides useful information regarding the effect of each process parameter on the workability required for high-temperature processes. Lowering the CSI value by controlling process variables, such as the temperature and strain rate, is recommended for a design free from process-induced cracks. More importantly, a coded finite element subroutine coupled with the CSI can help visualize local positions where cracks may be produced during a hot-working operation. For experimental validation, a Gleeble test was performed on Ti6Al4V specimens containing four notches with different depths. The successful application of the CSI to the process design of shop-floor unmanned aircraft components helped confirm the applicability and validity of this study.

Burst of Internally Pressurized Steel Torispheres

Abstract The paper begins with derivation of true stress–true strain data, including postnecking section. Available results of past uni-axial tests on round 10 mm diameter and 200 mm long mild steel samples are the basis of the conversion. The steel in question was used to manufacture ten torispherical domes that were in the past tested for burst. Hence, the relevance of matching material model is necessary for the finite elements (FE), analyses. In the past, plastic instability and constraints on the magnitude of plastic strains were postulated as criteria for the burst of internally pressurized torispheres. These criteria for burst pressure are being examined and benchmarked against the tests. The current paper, using the FE analyses, shows that modification of constraints on plastic strains has only marginal effect on the burst which still remains on the unsafe side of test data by a sizeable margin. The same is found to be true for plastic instability criterion. Subsequent computations moved back to the use of engineering stress–strain. Then, two types of computing are carried out here, based on multisegment and bilinear modeling of material. Computed results of burst pressure follow the test data to within (−6%, +10%). These results are far better than all the previous.

Characterization of Hot Workability in AISI 4340 Based on a 3D Processing Map

This study performed high-temperature compression tests at the temperature 900 to 1200 °C and strain rate 0.01 to 10 s−1 to characterize the high-temperature deformation behavior of AISI 4340. The constitutive equation of AISI 4340 was expressed using the Arrhenius model and the Zener–Hollomon (Z) parameter. Dynamic Recrystallization (DRX) behavior was evaluated by observing the compressed specimen with Electron Backscatter Diffraction (EBSD). The processing map is based on the dissipation efficiency of the dynamic material model (DMM) and the plastic instability criterion of Ziegler. At strain 0.4, the power dissipation efficiency value is 0.5 or more, and the instable zones are immediately identified through the processing map. The strain, strain rate and temperature data obtained from the FEM simulation of the hot forging process are displayed on the proposed 3D processing map to avoid the flow instability zones and ensure high power dissipation efficiency zones, allowing the operator to control the process’s temperature and speed.

Plastic instability criterion based on new necking parameters for Cu–Al, Cu–A5052, and Cu–A5083 roll-bonded laminated metal composites fabricated without post-annealing

Although laminated metal composites fabricated by accumulative roll bonding (ARB) undergo kink-band formation, there are no guidelines for optimizing their fabrication to avoid necking and shear localization without post-annealing. The necking of the composite layers during rolling generates non-uniformities that may degrade the mechanical performance of the composite. This paper proposes a model for laminated metal composites that aims to quantitatively assess and predict necking based on the work-hardening of each layer. Cu–Al-, Cu–A5052-, and Cu–A5083-laminated metal composites were fabricated using ARB at room temperature (~300 K) without post-annealing, and they were subjected to mechanical and microstructural analyses. A normalized neck amplitude was introduced as a new parameter that accurately predicted the degree of necking observed experimentally. Another new parameter, an instability index, was introduced to frame the necking criterion of the hard layers. A plastic instability criterion framed based on the new parameters accurately predicted the degree of necking in the hard layers of the as-prepared laminated metal composites. These findings may be applied to guide the fabrication of metal composites of any composition using the ARB process.

On a plastic instability criterion for ultra-large radial-axial ring rolling process with four guide rolls

A dynamic mechanical model is proposed to describe the complexing actions of all the rolls on the ring during the ultra-large radial-axial ring rolling (RARR) process with four guide rolls. Based on the model, the calculation models for bending moment and normal stress at any section of the ring are deduced by force method. If the maximum section bending normal stress exceeds the yield stress of the ring materials, the ring will be distorted thus leading to the instability of the RARR process. According to this, a plastic instability criterion for the ultra-large RARR process with four guide rolls is developed, based on which a mathematical model to calculate the critical guide force for avoiding plastic instability of ring is obtained. The influence rule of the position of guide roll on the dangerous ring section of plastic instability is revealed, from which it is found the dangerous ring section mainly appears at the radial and axial deformation regions and the contact positions of the guide rolls and ring. The optimized layout of guide roll around the ring in favor of stability is determined to be about α1 = 61° and α2 = 119°. The plastic instability criterion is proven to be reliable from the aspects of the critical guide force, the section bending moment and normal stress and the dangerous ring section of plastic instability. Intelligent simulation case studies for the RARR process of ultra-large aluminum alloy ring indicate that the stable forming of the process can be effectively realized by regulating the guide force based on the plastic instability criterion. This work could provide a valuable guidance for the control of guide rolls and the optimization of the ultra-large RARR process with four guide rolls.

Prediction of Crack Initiation Based on Energy Storage Rate during Low-Cycle Fatigue of Austenitic Stainless Steel.

The low-cycle deformation of 304L austenitic stainless steel was examined in terms of energy conversion. Specimens were subjected to cyclic loading at the frequency of 2 Hz. The loading process was carried out in a hybrid strain–stress manner. In each cycle, the increase in elongation of the gauge part of the specimen was constant. During experimental procedures, infrared and visible-range images of strain and temperature fields were recorded simultaneously using infrared thermography (IR) and digital image correlation (DIC) systems. On the basis of the obtained test results, the energy storage rate, defined as the ratio of the stored energy increment to the plastic work increment, was calculated and expressed in reference to selected sections of the specimen. It was shown that, before the specimen fracture in a specific area, the energy storage rate is equal to zero (the material loses the ability to store energy), and the energy stored during the deformation process is released and dissipated as heat. Negative and close-to-zero values of the energy storage rate can be used as a plastic instability criterion on the macroscale. Thus, the loss of energy storage ability by a deformed material can be treated as an indicator of fatigue crack initiation.

Hot Deformation Constitutive Equation and Plastic Instability of 30Cr4MoNiV Ultra-High-Strength Steel

In this work, the hot deformation behavior of 30Cr4MoNiV ultra-high-strength steel is investigated by isothermal compression tests using the Gleeble-3500 thermal simulation machine (Dynamic Systems Inc., New York, NY, USA) at a temperature range of 1173–1373 K under the strain rate of 0.01–10 s−1. A constitutive equation with strain-dependent constants and processing maps suitable for 30Cr4MoNiV ultra-high-strength steel are established. The results show that the combination of the hyperbolic sine function and the Zener-Hollomon parameter can accurately represent the influences of deformation temperature, strain rate, and strain on the flow stress of the 30Cr4MoNiV ultra-high-strength steel. The applicability of plastic instability criteria such as , , , and the instability parameter ξ are analyzed, the stability and instability regions are clarified accurately, and the optimized processing regions are given in the stability regions. The optimized regions are verified by the uniform equiaxed grains, and the plastic instability is validated by dynamic strain aging and the microstructure of the voids.

Formability prediction using bifurcation criteria and GTN damage model

In this paper, four plastic instability criteria, which are based on the bifurcation theory, are coupled with the GTN damage model for the prediction of diffuse and localized necking. General bifurcation (GB) criterion and limit-point bifurcation (LPB) criterion are used to predict diffuse necking, while loss of ellipticity (LOE) criterion and loss of strong ellipticity (LOSE) criterion are used to predict localized necking. The resulting constitutive equations and instability criteria are implemented into the finite element code ABAQUS/Standard. The constitutive equations are formulated within the framework of large deformations and fully three-dimensional approach. Since the developed numerical tools have intended applications mainly for thin sheet metals; therefore, the plane-stress conditions are considered within the instability criteria. The present contribution focuses on the effect of destabilizing mechanisms, due to non-associative plasticity and non-normal plastic flow rule, on the prediction of forming limit diagrams (FLDs). Theoretical classification of the bifurcation criteria, in terms of their order of prediction of critical necking strains, is first presented. Then, several variants of the GTN model are combined with the bifurcation criteria for the prediction of FLDs for fictitious materials. It is shown that the hierarchical prediction order of the different instability criteria is consistent with the theoretical classification, for all the considered variants of the GTN model. More specifically, it is shown that the GB criterion provides a lower bound to all bifurcation criteria, in terms of necking prediction, while the LOE criterion represents an upper bound.

Experimental and numerical FEM-based determinations of forming limit diagrams of St14 mild steel based on Marciniak-Kuczynski model

Forming Limit Diagrams (FLD) are used to design metal sheet processes and to choose appropriate material according to their formability. Development of simple and robust methods to determine the formability domain is then a major industrial issue. Marciniak-Kuczynski (M-K) plastic instability criterion is a classical and common approach used to predict numerical FLD. A convergence of the experimental conditions and theoretical M-K hypotheses is investigated. This analysis leads in the proposition of a simple experimental procedure based on classical instrumented biaxial testing machines to reproduce M-K in-plane loading conditions. Experimental results are compared with numerical simulations based on a finite element method implantation of M-K model. This versatile implementation allows the coupling of the plastic instability criterion in ABAQUS with a large range of material behaviors. Application of these experimental and numerical procedures on commercial St14 mild steel leads to the relative differences between lower experimental points and numerical forming limits predictions that do not exceed 4% and 10% in the case of uniaxial and equibiaxial tension for initial prescribed defect ratio of 0.99 and 0.95, and 22% in the case of plane tension. These procedures constitute ways easily implementable in the industry to obtain FLD at reduced costs that show good correlations between experimental results and numerical M-K predictions.

Numerical investigation of necking in perforated sheets using the periodic homogenization approach

Due to their attractive properties, perforated sheets are increasingly used in a number of industrial applications, such as automotive, architecture, pollution control, etc. Consequently, the accurate modeling of the mechanical behavior of this kind of sheets still remains a valuable goal to reach. This paper aims to contribute to this effort by developing reliable numerical tools capable of predicting the occurrence of necking in perforated sheets. These tools are based on the coupling between the periodic homogenization technique and three plastic instability criteria. The periodic homogenization technique is used to derive equivalent macroscopic mechanical behavior for a representative volume element of these sheets. On the other hand, the prediction of plastic instability is based on three necking criteria: the maximum force criterion (diffuse necking), the general bifurcation criterion (diffuse necking), and the loss of ellipticity criterion (localized necking). The predictions obtained by applying the three instability criteria are thoroughly analyzed and compared. A sensitivity study is also conducted to numerically investigate the influence on the prediction of necking of the design parameters (dimension, aspect-ratio, orientation, and shape of the holes), the macroscopic boundary conditions and the metal matrix material parameters (plastic anisotropy, hardening).

Comparison of Predicted Forming Limit Curves with Measured Experimental Data on Hot-Dip Zinc-Coated Cold-Rolled Steel by Incremental Forming Process

Single Point Incremental Forming (SPIF) is a die-less forming process with advantages of high-flexibility, low-cost and short lead time. The high local strains that are applied to the metal sheet, often exceeding the conventional formability limit. This paper is focused on comparison of predicted forming limit curves with measured experimental data on Hot-Dip Zinc-Coated Cold-Rolled sheet, with 0.20 mm thick is studied in single point incremental forming. Truncated square pyramid and cone are formed to study the formability of blank sheets at room temperature. It was found that both Formulation of plastic instability criteria and Keeler’s formula gives the lowest FLC. FLDs have predicted failures in forming process consistently with the real experiments. The experimentally obtained cracking limit differ from analytical one and empirical one by about 3.398 and 2.135 true strain respectively at FLD0, the corresponding plane strain values.

Microstructure and texture development in Ti-15V-3Cr-3Sn-3Al alloy – Possible role of strain path

In the present investigation, evolution of microstructure and texture was studied for a β titanium alloy during cold rolling (unidirectional rolling (UDR) and cross rolling (multi-step cross rolling (MSCR) and two step cross rolling). For both UDR and MSCR of initially hot rolled alloy consisting of elongated and equiaxed grain structure, the occurrence of shear bands inside the grains was the main feature of the microstructure. The density of these shear bands was dependent on the cold rolling reduction and strain path and was found to be orientation dependent. Shear bands preferentially occurred in γ-fiber (normal direction (ND)//〈111〉) oriented grains. The regions with shear bands had higher hardness than the regions without shear bands, and {111}〈112〉 component of the γ-fiber was found to be more susceptible to formation of shear bands. The orientation dependence of these shear bands was analyzed within the framework of Dillamore's plastic instability criterion. During UDR, strong α and γ-fibers were observed after highest strain (ε = 1.6), while strong rotated cube ({100}〈110〉) texture developed after MSCR at highest strain (ε = 1.6). The volume fraction of both α and γ fibers gradually increased with the increase in cold rolling reduction during UDR. For MSCR, the rotated cube component gradually increased with increase in cold rolling reduction. In solution annealed β-Ti alloy with equiaxed grain structure, α and γ fibers were formed after highest strain (ε = 1.6) during UDR. However, due to large grain size, both α and γ fibers were discontinuous. The texture development was found to be more strongly dependent on the strain path than the initial microstructure during cold rolling.

Forming-limit strains of perforated steel sheets under biaxial stress state

The forming-limit strains of cold-rolled steel sheets perforated with regularly arranged round-, square-, and cross-shaped holes were experimentally and theoretically estimated. Two types of hole arrangements, i.e. square and triangular patterns, were considered for each hole shape and the experimental forming-limit strains were determined using the hemispherical dome test (also known as Nakazima test). The theoretical forming-limit curves were computed using the finite element method with Hill's quadratic yield function and a plastic instability criterion determined from the external force power. By comparing the experimental results and theoretical calculations under proportional loading, the formability prediction performance of the theoretical approach was evaluated. It was found that although the approach is not applicable for the triangular array of cross-shaped holes, it can achieve partially acceptable prediction for the other cases.

Prediction of necking in thin sheet metals using an elastic–plastic model coupled with ductile damage and bifurcation criteria

In this paper, the conditions for the occurrence of diffuse and localized necking in thin sheet metals are investigated. The prediction of these necking phenomena is undertaken using an elastic–plastic model coupled with ductile damage, which is then combined with various plastic instability criteria based on bifurcation theory. The bifurcation criteria are first formulated within a general three-dimensional modeling framework, and then specialized to the particular case of plane-stress conditions. Some theoretical relationships or links between the different investigated bifurcation criteria are established, which allows a hierarchical classification in terms of their conservative character in predicting critical necking strains. The resulting numerical tool is implemented into the finite element code ABAQUS/Standard to predict forming limit diagrams, in both situations of a fully three-dimensional formulation and a plane-stress framework. The proposed approach is then applied to the prediction of diffuse and localized necking for a DC06 mild steel material. The predicted forming limit diagrams confirm the above-established theoretical classification, revealing that the general bifurcation criterion provides a lower bound for diffuse necking prediction, while the loss of ellipticity criterion represents an upper bound for localized necking prediction. Some numerical aspects related to the prestrain effect on the development of necking are also investigated, which demonstrates the capability of the present approach in capturing the strain-path changes commonly encountered in complex sheet metal forming operations.

Prediction of Localized Necking Based on Crystal Plasticity: Comparison of Bifurcation and Imperfection Approaches

In the present work, a powerful modeling tool is developed to predict and analyze the onset of strain localization in polycrystalline aggregates. The predictions of localized necking are based on two plastic instability criteria, namely the bifurcation theory and the initial imperfection approach. In this tool, a micromechanical model, based on the self-consistent scale-transition scheme, is used to accurately derive the mechanical behavior of polycrystalline aggregates from that of their microscopic constituents (the single crystals). The mechanical behavior of the single crystals is developed within a large strain rate-independent constitutive framework. This micromechanical constitutive modeling takes into account the essential microstructure-related features that are relevant at the microscale. These microstructural aspects include key physical mechanisms, such as initial and induced crystallographic textures, morphological anisotropy and interactions between the grains and their surrounding medium. The developed tool is used to predict sheet metal formability through the concept of forming limit diagrams (FLDs). The results obtained by the self-consistent averaging scheme, in terms of predicted FLDs, are compared with those given by the more classical full-constraint Taylor model. Moreover, the predictions obtained by the imperfection approach are systematically compared with those given by the bifurcation analysis, and it is demonstrated that the former tend to the latter in the limit of a vanishing size for the initial imperfection.

Structural developments in un-stabilized ultra low carbon steel during warm deformation and annealing

In the present investigation, ultra low carbon steel samples were deformed in plane strain compression mode in a deformation simulator. The deformation was carried out at four different temperatures in the warm rolling region (293, 473, 673 and 873 K) upto 70% strain at two different strain rates (0.1/s and 1/s). Subsequently, all the deformed samples were fully recrystallized at 1073 K. Afterwards, all the deformed and fully recrystallized samples were subjected to detailed microstructural characterization using optical microscope, scanning electron microscope and electron backscattered diffraction. Bulk texture was measured for all the samples by X-ray diffraction. In-grain misorientation developments (kernel average misorientations) were estimated for the deformed γ-fibre (ND//<111>) and α-fibre (RD//<110>). Deformed γ-fibre showed an increase in in-grain misorientation at intermediate deformation temperatures. This increase was explained by using the plastic instability criterion. After complete recrystallization, the γ-fibre strengthened for deformation at lower temperatures (293 K and 473 K), while Goss texture developed for samples deformed at higher temperatures (673 K and 873 K).

Evaluation of EM loads distribution on DEMO blanket segments and their effect on mechanical integrity

This work is aimed to analyze the EM internal forces distribution on the blanket system (blankets modules and segment back supporting structure) of the EU PPPT DEMO 2015 reactor configuration. In order to validate their impact on the segment structure, an EM analysis is conducted using a simplified plasma central disruption. The calculated Lorentz’s forces distributions are then used as input for structural analyses focusing on the mechanical integrity of the segment back supporting structure. In particular, the electrical and structural assumptions used in this work are based on the HCPB blanket design developed at the Karlsruhe Institute of Technology. A preliminary assessment of the primary stresses according the design code RCC-MRx indicates the ability of the segments to resist the EM forces, where the lowest margin is given by the immediate plastic instability criterion on the inboard segment with 14%.

Forming-limit prediction of perforated aluminium sheets with square holes

The forming-limit strains of perforated aluminium alloy (AA5052-O) sheets with square holes were theoretically and experimentally estimated for two types of hole arrangements: square and triangular patterns. The theoretical forming-limit curves were obtained by finite-element analyses on a unit module of the perforated sheets using two different approaches: the phenomenological theory and crystal plasticity theory. Hill’s quadratic anisotropic and von Mises yield functions were used for the phenomenological analysis, and the one-element-per-grain model was adopted for the crystal plasticity analysis. To determine the forming limits, two different types of plastic instability criteria were applied. The experimental forming-limit strains were also obtained through a Nakazima stretching test. The theoretical predictability of the forming-limit curves was assessed by comparing the theoretical and experimental results. The comparison demonstrated that (1) the plastic instability criterion based on the external force power predicted qualitatively the same forming-limit curves as the criterion based on the equivalent plastic strain of the ligament for both hole arrangement patterns and (2) although the shapes of the predicted forming-limit curves were in reasonable agreement with the experimental results, the level of the predicted limit strains was considerably higher than that of the experimental limit strains. Thus, it was found that neither of the plastic instability criteria previously proposed for perforated sheets is appropriate to characterise the formability of perforated aluminium sheets with square holes.

Investigation and comparative analysis of plastic instability criteria: application to forming limit diagrams

The prediction of forming limit diagrams (FLDs) is of significant interest to the sheet metal forming industry. Although a large variety of plastic instability criteria have been developed during the previous decades, there is still a lack of comparison of their respective theoretical bases. The aim of this paper is to present the theoretical formulations of a representative selection of diffuse necking and strain localization criteria based on the maximum force principle, the Marciniak–Kuczyński method and the bifurcation approach. The theoretical foundations and underlying assumptions for each criterion are specified prior to their application to several materials to determine the associated FLDs. The capability of the criteria to predict the formability of thin metal sheets is discussed and a classification of some of the criteria is attempted according to their order of occurrence in terms of the localization prediction.