Equivalent Plastic Strain Research Articles

Evolution of yield behavior for AA6016-T4 and DP490—Towards a systematic evaluation strategy for material models

Uniaxial and cruciform biaxial tensile tests are performed on a face-centered cubic material AA6016-T4 and a body-centered cubic material DP490 under 19 different loading paths, i.e., uniaxial tension in seven directions, simple shear along the rolling direction, and biaxial tension in rolling/transverse and 45°/135° directions, with seven and four stress ratios, respectively. The ability of several yield criteria to describe the plastic anisotropy for the tested materials, under the associated and non-associated flow rules, is evaluated systematically. A new evaluation strategy to check the validity and applicability of the material models is proposed in this study. This strategy is different from the traditional evaluation strategy in that the biaxial tensile mechanical properties measured in the 45°/135° sampling direction are included in the investigation scope, and it is not limited to the rolling/transverse sampling direction, i.e., the yield stress functions are evaluated by comparing the experimental and predicted uniaxial yield stresses and plastic work contours on the normal and diagonal planes. Further, the plastic potential functions are confirmed by the description accuracy of uniaxial rα-values and the directions of plastic strain rate in the rolling/transverse and 45°/135° directions. A new analytical calibration program is developed for the material parameters of the Poly6 yield criterion related to normal (a1,a2,...,a7) and shear stress components (a8,a9,...,a16), which can further introduce the yield stresses under the near plane strain states (σPS0, σPS45, and σPS90) and pure shear yield stress along the rolling direction (τ0). The results indicate that the new calibration strategy of Analytical Poly6-II&2 can accurately describe the anisotropic yield behavior of the tested materials compared with other advanced yield criteria, especially for plastic work contours on the diagonal plane. Significant anisotropic yield behavior was observed under biaxial tensile stress states with the same loading ratio in different sampling directions. Therefore, investigating the prediction accuracy of the biaxial tensile mechanical properties in only the rolling/transverse sampling direction is insufficient for evaluating the effectiveness of the material models; the mechanical properties at the initial yield point cannot fully reflect the plastic anisotropy of the materials. The material parameters of the Analytical Poly6-II&2 yield criterion are expressed as functions of equivalent plastic strain, which can continuously capture the evolution of the anisotropic yield behavior for AA6016-T4 and DP490. Three different calibration strategies of the material parameter a16 are evaluated in this study. These strategies do not affect the description ability of the uniaxial yield stresses, rα-values, and plastic work contours on the normal plane; however, they influence the calculation results of plastic work contours on the diagonal plane. For attaining a balanced prediction accuracy, it is recommended to provide the values of both τ0 and σPS45.

Prediction of the Interface Deformation of Ultrasonic Spot Welding of Multilayer Metal Foils Considering Energy Gradient

Abstract The ultrasonic spot welding (USW) is widely used in the joining of multilayer Cu or Al tabs in the lithium-ion battery. Due to the high-frequency vibration of the sonotrode and various deformation in each interface, the friction behavior is complex which makes it difficult to simulate the welding process of multilayer specimens. In this paper, an efficient and accurate finite element model (FEM) was proposed via introducing the interface heat flux to equivalent the heat generation by the friction. The total heat flux was determined by the heat transfer analysis and the proportion of each interface was determined based on the analysis of the friction behavior. Then, the FEM was validated by comparing the simulated temperature and deformation with experimental results. Finally, the FEM was applied to simulate the USW process of four, five, and ten layers of copper and aluminum foils in order to characterize the gradient of the ultrasonic energy. It was found that the heat generation concentrated in middle interfaces was 65% of the total in the welding of four-layer copper foils. The heat generation was mainly related to the welding parameters and the proportion was related to the size of tips and the structure of specimens. The plastic strain varied in specimens because of the gradient of the input energy. It was most obvious in the welding of 10-layer aluminum foils that the maximum equivalent plastic strain (PEEQ) in the fifth interface was 92.9% smaller than the top interface.

Determination of Safety Factor for Rock Mass Surrounding Tunnel by Sudden Change of Equivalent Plastic Strain in Strength Reduction Method

The safety factor of rock mass surrounding tunnel can be determined using the strength reduction method (SRM), furthermore, it is very important to solve the criterion of critical state. For the stability estimation of rock mass surrounding tunnel, there is need to discuss that it is preferable to use the same criteria for the slope stability, such as non-convergence of finite element calculation, penetration of plastic strain and sudden change of horizontal displacement. The safety factor can be determined by sudden change of equivalent plastic strain in relationship between a reduction coefficient of strength parameter and equivalent plastic strain. This method is based on the elasto-plastic finite element method (FEM) and the SRM by ABAQUS and Mohr–Coulomb yield criterion. Simulation results using this method show how a safety factor varies with geometries, friction angles and cohesions for circle and square tunnels. Simulation results also show the safety factor varying with quality change of rock mass, pore water pressure and tunnel depth.

Multiple ballistic impacts of thin metallic plates: Numerical simulation

The ballistic performance of protective structures under multiple projectile impacts attracts increasing attention due to its practical importance, and existing studies were seldomly devoted to exploring how the structure would deform and fail when subjected to such loads. This study aimed to characterize the multi-hit ballistic resistance of fully-clamped thin plates made of 304 stainless steel using finite element method, with the equivalent plastic strain employed to define material damage and failure/fracture. The numerical model was validated against existing experimental results of double impacts at the same location, with good agreement achieved. The model was subsequently employed to quantify the effects of impact position, interval time between successive hits, projectile nose shape (e.g., spherical, flat, and conical), and boundary condition of target plate on ballistic limit and deformation/failure modes. Further, ballistic limit boundaries were constructed for both double and triple impacts of projectiles. Obtained results are helpful for designing high-performance protective structures against multiple projectile impacts.

Strength and Failure of Self-Piercing Riveted Aluminum and Steel Sheet Joints: Multi-axial Experiments and Modeling

The mechanical failure of self-piercing rivet (SPR) joints connecting seven series aluminum and high strength steel sheets is investigated, both numerically and experimentally. The joint strength and failure mechanisms are characterized for a total of four distinct loading modes, including the lap-shear, cross-tension, inclined cross tension and coach peel. For the analysis of the underlying influential parameters in each loading case, joint designs with equal total sheet thickness and equal rivet head diameters are considered. The highest strength values are obtained in lap-shear loading for all joint types, while high rivet interlock joints are observed to pair with increased cross-tension strength values. Moreover, the loading mode in which the highest energy is absorbed directly relates to the joint type. Depending on the material combination to be joined, either the cross-tension or the coach-peel cases yielded the highest energy absorption. The experimental results indicate that high rivet hardness and bottom sheet strength values have a favorable impact on the coach-peel strength and the associated deformation response. For all failure modes, the lowest rivet hardness employed (H4) was proven sufficient to prevent rivet failure in the joint types employed, despite the substantial equivalent plastic strains developed in it. Furthermore, high interlocks were noted to primarily affect the lap shear failure mode, inducing significant bottom sheet damage upon fracture, with the failure response observed in all other loading cases to remain practically insensitive to the interlock magnitude.

Deformation characteristics and formability enhancement during ultrasonic-assisted multi-stage incremental sheet forming

Although the multi-stage incremental sheet forming strategy is beneficial for manufacturing complex geometrical shapes via objective transitional stages, the forming limit and geometric accuracy are highly dependent on intermediate shapes, which need further improvement. Therefore, a novel forming strategy by combining the multi-stage sheet forming with ultrasonic-assisted vibration (UV) was proposed in the present work. This paper investigates the effect of ultrasonic vibrations on forming forces, thickness distribution, and stress–strain distribution through experimental tests and finite element (FE) simulations. Initially, a series of tests were conducted to determine the forming limit for three proposed strategies based on parameters including depth, initial diameter, and angle, both with and without the assistance of UV. Afterward, the FE model was established in ABAQUS/Explicit based on the optimal strategy by adopting the modified crystal plasticity constitutive model. The results indicated that, after superimposing the ultrasonic vibration, forming forces were effectively reduced and plastic deformation was greatly improved due to the increased equivalent plastic strain. Meanwhile, the application of the UV field efficiently reduces the high-stress zones and significantly decreases the stress value. Finally, it was discovered that by imposing UV at the appropriate forming stages, formability and thickness distribution can be successfully improved. The present investigation is beneficial to well understand the affecting mechanism of UV in completing the multi-stage sheet forming technique and obtaining the enhanced sheet formability.

A coupling model of element-based peridynamics and finite element method for elastic-plastic deformation and fracture analysis

An element-based peridynamics (EBPD) and finite element method (FEM) coupling model is proposed to solve the elastic-plastic deformation and failure problems. The FEM and EBPD are used in the boundary region and the interior elastic-plastic crack growth region, respectively. A scheme is proposed to improve the computation efficiency of EBPD by deleting the bad quality elements in the horizon of each PD node. EBPD has the non-local stress and non-local strain concepts to conveniently describe the yield stress and equivalent plastic strain, and does not have instability problems. The elastic-plastic computation framework is used in the coupling model solved by the incremental method to calculate the elastic-plastic deformation and failure process. The coupling model can calculate the elastic-plastic problem with the linear and nonlinear hardening laws. A 2D elastic-plastic crack propagation process is also simulated by the proposed coupling model.

Evaluating the strength of grade 10.9 bolts subject to multiaxial loading using the micromechanical failure index: MCEPS

AbstractBolted joints in steel structures are generally subject to combined actions. The research on ultimate capacity of bolted joints under combined tension and shear actions, twin shear actions, and combined tension‐twin shear actions is relatively limited. The aim of this paper is to calibrate the fracture locus of grade 10.9 bolts using the mesoscale critical equivalent plastic strain (MCEPS). We use ductile fracture simulation to numerically evaluate the ultimate resistance of bolts subject to multiaxial loading and compare the results with the current design standards. The results show that predictions for grade 10.9 bolts subject to multiaxial loading in Chinese code GB 50017 and American code AISC‐360 are not on the safe side, while predictions in European code EN1993‐1‐8:2005 are slightly on the conservative side. We propose two modification factors to improve prediction of bolt strength subject to multiaxial loading; namely the multiaxial loading factor for shear resistance ξv and the multiaxial loading factor for tensile resistance ξt.

Study on the mechanical performance of a three-layered wire rope strand with a surface pit in varied corrosion direction into the wire

Pitting corrosion often occurs in wire rope strands under harsh service environments, causes material removal and local stress concentration, and has been an important trigger for the failure of the strands. In this paper, the spatial parameter equations of wires in each layer of a three-layered wire rope strand with a corroded outermost wire are derived. Based on the equations, the high-precision finite element model of the corroded strand with varied corrosion direction into the wire is established with the consideration of the elasto-plasticity of the wire material. Then axial tensile simulations of the strand are performed to analyze the influence of the surface pit on the mechanical properties, including the contact characteristics, the stress-strain characteristics, the elastoplastic characteristics and the axial load-bearing characteristics, of the strand. The results show that the stress concentration is obvious in the corrosion area, and the maximum stress and plastic strain of the strand occur in the pit. The existence of corrosion pit decreases the bearing capacity of the strand, while increases the contact pressure, von Mises stress, and equivalent plastic strain of the strand significantly. The maximum von Mises stress, maximum plastic strain, stress concentration factor, maximum contact pressure and the decrement of bearing capacity increase with increasing circumferential inclined angle of the pit, while decrease with increasing axial inclined angle of the pit.

A novel process for manufacturing large-diameter thin-walled metal ring: Double-roll pendulum hot rotary forging technology

Large-scale thin-walled metal ring parts are the key main structural parts in new energy sources and aerospace equipment. How to form reliable large-diameter thin-walled metal rings has become the focus of attention of researchers. This paper proposes a double-roll pendulum hot rotary forging (DRPHRF) process for forming such components and demonstrates the feasibility of forming rings with a diameter of 4 m and a thickness of 0.1 m (axial) using this process. The forming process of DRPHRF is analyzed and designed, and the critical instability and forming conditions are obtained. The finite element model of the ring DRPHRF was established in the DEFORM-3D software using the scale-down process with a ratio of 10:1, and the accuracy of the model was verified through experiments. Based on the reliable finite element model, the deformation behavior of the ring DRPHRF is analyzed. The results show that each part of the ring is subjected to periodic stress, which reduces the residual stress. The uniform circumferential equivalent plastic strain (PEEQ) distribution and the characteristics that the axial PEEQ becomes uniform as the thickness decreases are conducive to forming a thin-walled ring with uniform performance. There is less heat loss during the forming process, which is beneficial to reduce the stress during forming.

Analysis of Strain Inhomogeneity in Extruded Al 6061-T6 Processed by ECAE

This paper presents an analysis of the test and simulation of the equal channel angular extrusion (ECAE) of a commercial Al 6061-T6 alloy previously extruded. Special emphasis is given to the analysis and comparison of the simulated values and distribution of equivalent plastic strain with those calculated with analytical models across the height of the middle section of the deformed billet. The results reveal the limitations of the analytical models when the effects of the inner die corner and curvature of the outer wall on the material response during the test are considered for the ECAE device used in this work. Specifically, in the simulations performed in this work, the plastic deformation zone, far from being uniform, extends along with the height of the billet where, in particular, near the inner wall over the inlet and outlet channels, even in the central region of the billet, the equivalent plastic strain is not homogeneous or discontinuous, varying mainly due to the effect of the curvature of the outer channel.

Study on Seismic Response and Damping Performance of Tunnels with Double Shock Absorption Layer

Shock absorption layer is an effective measure to decrease damage of tunnels under earthquake. According to previous work, the smaller stiffness of damping material, the better damping effect of the tunnel. In order to meet the actual engineering requirements, the shock absorption layer is applied to the upper part of tunnels (not including the invert), which is called a local shock absorption layer. This study is to analyze the damping effect of different types of local shock absorption layers based on the dynamic nonlinear time-history numerical analysis. Six real ground motions with different dominant frequencies are selected, their peak ground accelerations (PGA) are set to 0.2 g, 0.4 g, 0.6 g, and 0.8 g, respectively. The damage index and total dissipated energy of secondary lining, and equivalent plastic strain of surrounding rock are used as indicators to reflect the damping performance of the local shock absorption layer. Numerical results highlight that the damping performance with double local shock absorption layer is the best, and the damping performance of shock absorption layer under large earthquake is better than that under small earthquake.

Finite element analysis of the thermo-mechanical fatigue of DD8 single crystal nickel-based superalloy

Abstract A nonlinear finite element method is presented for analysing the thermo-mechanical fatigue behavior of the DD8 single crystal nickel-based superalloy. The specimens had axial orientations along the [001] direction. In-phase and out-of-phase thermo-mechanical fatigue were simulated under mechanical strain control with a temperature variation from 450 to 900 °C. The cyclic mechanical behavior, the equivalent stress and plastic strain were investigated in both γ' phase and γ matrix.

Study on welding crack sensitivity assessment method based on thermal elastic plastic finite element analysis

This study presents a new welding crack sensitivity assessment method with the equivalent plastic strain increment as an indicator, and the reliability is verified by comparing the computed results and experimental results of bead-on-plate joint under different welding conditions. Then the proposed method is applied to assess the welding crack sensitivity of multi-pass joints in the bridge rehabilitation engineering. The results show that the equivalent plastic strain increment increases with increasing heat input and constraint degree, and decreases with increasing preheat temperature. The equivalent plastic strain increment can be used as an indicator for assessing welding crack sensitivity assessment of joints. With regard to multi-pass welded joints, the welding crack sensitivity decreases with the increase of number of weld passes in terms of equivalent plastic strain increment. The welding crack sensitivity assessment method proposed in this study is reliable and can provide a practical tool for assessing the performance of welded joints.

Effects of configuration parameters on the deformation and fracture behaviors of TiB2/Cu composites with network structure: A numerical approach using an enhanced finite element model

In order to reflect the real network composites with a hard phase TiB2 surrounded by a soft phase Cu, a developed large crystal-like cell model which closer to the real cell structure is proposed in this paper. Micro-geometric features of network TiB2/Cu composites are extracted based on the actual SEM, and a stochastic synthesis algorithm is adopted to reconstruct network structure. Based on MATLAB, a 3D network model of TiB2/Cu composites is established through Voronoi algorithm. By using finite element method, the effects of configuration parameters including TiB2 particle wall thicknesses, matrix phase sizes and matrix phase morphology on the deformation and fracture behaviors in network TiB2/Cu composites are investigated, and the mechanical properties of the composites are predicted. Three failure modes including brittle fracture of particle wall, ductile damage of matrix and traction-separation law of interface are introduced in the proposed models. The experimental stress–strain curves were implemented to verify the simulation results. The results show that the trend is in good agreement and the simulation results are stable and reliable. The comprehensive mechanical properties of network composites are assessed by yield strength, elastic modulus, elongation and tensile strength. The equivalent stress and stress concentration factor of the particle wall, brittle fracture process of network, interfacial debonding, crack damage and equivalent plastic strain of matrix are quantitatively presented. It is illustrated that the bearing capacity of network TiB2/Cu composites is determined by Cu matrix, TiB2 particle wall and interface. A macro and micro structure-properties relationship of network configuration composites is established in this paper. This work provided reference and guidance for the configuration design of the network composites in the experiment.

Precise dynamic finite element elastic-plastic seismic analysis considering welds for nuclear power plants

This study performed a precise dynamic finite element time history elastic-plastic seismic analysis considering the welds, which have been not considered in design stage, on the nuclear components subjected to severe seismic loadings such as beyond-design basis earthquakes for sustainable nuclear power plants. First, the dynamic finite element elastic-plastic seismic analysis was performed for a general design practice that does not take into account the welds of the pressurizer surge line system, one of safety class I components in nuclear power plants, and then the reference values for the accumulated equivalent plastic strain, equivalent plastic strain, and von Mises effective stress were set. Second, the dynamic finite element elastic-plastic seismic analyses were performed for the case of considering only the mechanical strength over-mismatch of the welds as well as for the case of considering both the strength over-mismatch and welding residual strain. Third, the effects of the strength over-mismatch and welding residual strain were analyzed by comparing the finite element analysis results with the reference values. As a result of the comparison, it was found that not considering the strength over-mismatch may lead to conservative assessment results, whereas not considering the welding residual strain may be non-conservative.

Friction Coefficient Effect on Stress-Strain Distribution of Ceramic Coated Aeroengine Substrate Using Finite Element Analysis

This study presents the investigation of friction coefficient effect on stress-strain distribution of ceramic coated aeroengine specific material substrate using explicit finite element method. Half-cylinder-on-flat contact configuration subjected to normal and tangential loading is examined. Elastic ceramic coated elastic-plastic Ti-6Al-4V and Super CMV substrates are assigned to study the influence of different friction coefficient on contact pressure, von Mises stress, tangential stress and equivalent plastic strain distribution. The outcome of present research is quite revealing that stress-strain distribution response is remarkable for sliding step which experiencing significant traction compared to normal loading step. Higher possibilities of coated substrate equivalent plastic strain (plastic deformation) are registered under higher friction coefficient cases due to substantial resistance to overcome relative to tangential motion of contacting bodies.

An Investigation of a New Parameter Based on the Plastic Strain Gradient to Characterize Composite Constraint around the Crack Front at a Low Temperature.

Stress corrosion cracking (SCC) is an important destruction form of materials such as stainless steel, nickel-based alloy and their welded components in nuclear reactor pressure vessels and pipes. The existing popular quantitative prediction models of SCC crack growth rate are mainly influenced by fracture toughness values KJc or Jc. In particular, the composite constraint, containing the in-plane constraints and out-of-plane constraints around the crack front, has a significant influence on the fracture toughness of structures in nuclear power plants. Since the plastic strain gradient is a characterization parameter of the quantitative prediction model for crack growth rate, it may be a characterization parameter of composite constraint. On the basis of the experimental data at a low temperature of alloy steel 22NiMoCr3-7 used in nuclear pressure vessels, the gradient of equivalent plastic strain DPEEQ around the crack fronts at different constraint levels was calculated using the finite element method, which introduces a new non-dimensional constraint parameter Dp, to uniformly characterize the in-plane and out-of-plane constraint effects. Compared with constraint parameters APEEQ or Ap, the process of obtaining parameters DPEEQ or Dp is much simpler and easier. In a wide range, a single correlation curve was drawn between parameter Dp and normalized fracture toughness values KJc/Kref or Jc/Jref of specimens at a low or high constraint level. Therefore, regardless of whether the constraint levels of the structures or standard specimens are low or high, constraint parameter Dp can be used to measure their fracture toughness. To build an evaluation method that has structural integrity and safety while containing the composite constraint effects, in addition to accurate theoretical interpretation, further verification experiments, numerical simulations and detailed discussions are still needed.

Dynamic constitutive model of U75VG rail flash-butt welded joint and its application in wheel-rail transient rolling contact simulation

Rail welded joint is one of weak links in high-speed railway, and its dynamic performance has important effects on the safety, stability, and comfort of the high-speed train. In this work, the dynamic mechanical responses at different regions of U75VG rail flash-butt welded joint were investigated. The results show that the base metal (BM), welding zone (WZ), and heat-affected zone (HAZ) of U75VG rail flash-butt welded joint has an obvious strain rate effect, i.e., the material strength increases with increasing the loading strain rate. The strength of WZ is similar to that of BM, but its toughness is much lower than that of BM. The toughness of HAZ is the same as that of WZ, but its strength is much lower than that of BM and WZ. Based on the experimental results, an improved dynamic constitutive model was established to reasonably simulate the stress–strain curves of different regions from quasi-static loading to dynamic loading. Finite element (FE) analysis of transient rolling contact between rail welded joint and wheel under different conditions was performed. Compared with the results from quasi-static wheel-rail contact simulation, the equivalent plastic strain at each region of rail welded joint increases significantly and presents non-uniform distribution after considering the dynamic effect. When the wheel contacts the junction between different regions, the impact will cause a significant stress concentration at the rail welded joints. The maximum wheel-rail load by the implicit dynamic analysis is about 4 ∼ 12 times that obtained by the quasi-static analysis. Moreover, the maximum contact pressure, equivalent stress and equivalent plastic strain of each area of rail welded joints gradually increase with the increase in axle load and driving speed.

Doom-roof steel tanks under external explosion: Dynamic responses and anti-explosion measures

Large-scale cylinder storage tank is a kind of typical thin shell space structure, which is widely used in the storage of petrochemical products such as LNG, LPG and so on. The dynamic responses and failure process for steel tank under external explosion shock wave are complex dynamic problems with strong instantaneity, strong non-linearity and strong coupling. In this paper, a coupled analysis model was developed for simulating the dynamic responses of tank under external ground explosion. Compared with experimental datas which were given in existing relevant studies, the validity for numerical model and accuracy for simulation results were verified. Dynamic response for typical cylindrical tank was obtained through coupled numerical simulation, and the influences of scaled distance and tank wall thickness were studied through parameter analysis. Based on the simplified model of explosion loading on tank, the difference of dynamic response between uncoupled model and coupled model was analyzed. The anti-explosion effect for different parameters of anti-explosion bands on tank under external explosion was finally compared. The results show that: 1) The lower two layers tank wall firstly appear inward concave deformation and local plastic state. With the shock wave propagating upward along tank wall, the concave deformation and plastic strain of the front surface of tank wall increase obviously, and the maximum deformation region moves up to the middle part of tank wall, while the maximum plastic region basically remains at the lower part of tank wall. 2) Both the changes of scaled distance and tank wall thickness have significant influences on the deformation and equivalent plastic strain for steel storage tank. The maximum equivalent plastic strain and fracture failure mode generally appears at the lower part of tank wall firstly. The increase of the tank wall thickness is an effective measure to reduce the deformation and plastic strain for tank, and strengthen the anti-explosion performance for tank. 3) Due to the obstacle effect of the anti-explosion bands, the maximum equivalent plastic strain region moves from the bottom part of tank wall to the middle and upper part of tank wall. The displacement and equivalent plastic strain for steel tank decrease with the increase of cross-section and spacing for anti-explosion bands, and the effect of the former (increase height only) is relatively better.