Equivalent Plastic Strain Research Articles

A Modified Micro-Macro Constitutive Model for Porous Rocks with Pressure-Sensitive Matrix by considering a New Hardening Law

This paper aims mainly at providing an incremental elastoplastic constitutive model for heterogeneous porous rock-like materials in the frame of micromechanics. The studied material is considered to be made up of randomly distributed spherical pores embedded in a pressure-sensitive solid matrix obeying Drucker–Prager yield function. The effective elastic properties of porous rocks are obtained by the use of Mori and Tanaka homogenization scheme, which are on function of the bulk and shear moduli of the solid matrix and of the value of porosity. For the macroscopic nonlinear phase, a limit analysis-based macroscopic criterion is adopted to derive the basic constitutive rule by considering an associated plastic flow rule. In order to capture the typical hardening effects of rocks, an originally proposed hardening function of the solid matrix is also taken into consideration, which is related on the accumulated equivalent plastic strain. In order to verify its accuracy, the proposed micro-macro constitutive model is implemented by a numerical procedure including elastic predictions and plastic corrections and compared to experimental results of triaxial compression tests of sandstone with different confining pressures. It is observed that the numerical simulation is in accord with the experimental data, indicating that the obtained model is able to predict the main mechanical behaviours of rock-like materials.

Investigation of the Thickness Differential on the Formability of Aluminum Tailor Welded Blanks

A finite element model is proposed to investigate the effect of thickness differential on Limiting Dome Height (LDH) testing of aluminum tailor-welded blanks. The numerical model is validated via comparison of the equivalent plastic strain and displacement distribution between the simulation results and the experimental data. The normalized equivalent plastic strain and normalized LDH values are proposed as a means of quantifying the influence of thickness differential for a variety of different ratios. Increasing thickness differential was found to decrease the normalized equivalent plastic strain and normalized LDH values, this providing an evaluation of blank formability.

Indentation behavior of metal matrix composites reinforced with arbitrary shape particle using a coupled FE-EFG approach

The effect of particle volume fraction, size, and shape on the indentation behavior of particulate composites is investigated using coupled FE-EFG approach. A systematic approach is presented where the particles are modeled only in a small region under the indenter and the homogenized properties are assigned to the remaining region. Equivalent properties are determined using RVE analysis. Von-Mises criterion along-with updated Lagrangian approach is employed to capture elastoplastic large deformation behavior. Node-to-segment contact algorithm is adopted to model the contact behavior between indenter and matrix. Results in-terms of residual von-Mises stress, equivalent plastic strain, and deformed surface profile are presented.

Seismic performance of eccentrically braced frames with low-yield welded hollow spheres

In this study, an eccentrically braced frame with a low-yield welded hollow sphere was proposed. The structural model was established using ABAQUS software and analysed under monotonic and low-cyclic loading. We analysed the seismic performance, energy dissipation capacity, bearing capacity, secant stiffness, initial stiffness, deformation mode of the structure as well as welded hollow sphere and the fracture behaviour of the structure under monotonic and low-cyclic loading. The analysis revealed that the eccentrically braced frame with the low-yield welded hollow sphere exhibited good seismic performance. The deformation of the structure was mainly concentrated at the bottom of the frame column, low-yield welded hollow sphere, and weak points of both ends of the beam. The deformation of the low-yield welded hollow sphere was larger under the tension and pressure of the brace member. The wall thickness of the welded hollow sphere had a considerable influence on the structural performance. For a greater wall thickness of the welded hollow sphere, the bearing capacity, secant stiffness, energy dissipation capacity, and initial stiffness of the structure were greater, while the deformation of the sphere was smaller. Furthermore, equivalent plastic strain analysis demonstrated that the structure fractured most easily at the junction of the welded hollow sphere and supporting member.

Application of stress gradient plasticity model in different passivated problems

In this study, the theory of low-order stress-gradient plasticity deformation is considered to model elastic and plastic size-dependent deformation. In classical plasticity models, the physical length scale is not considered to control the size effects. Strain gradient plasticity models include one or more length scales that control size effects. Stress gradient plasticity model is introduced with a specific physical length scale and does not include any additional parameters. Torsion of a hollow tube, pure shear of a slab and torsion of a rod with and without passivation is modeled by considering elasto-plastic hardening model. The effects of passivation on materials deformation are studied. By increasing the material length scale and keeping the other parameters constant, the average equivalent plastic strain is decreased and the average stress is increased, as well as the hardening rate of the stress-strain curves. The obtained results are compared with the experimental results of Liu et al. (2013) and the results obtained from the theory of strain gradient plasticity for different problems (Niordson and Hutchinson, 2003; Lubarda, 2016; Hua and Liu, 2020). The results of the Stress gradient plasticity model is also compared with the strain gradient plasticity models.

Autonomous Development of a Machine-Learning Model for the Plastic Response of Two-Phase Composites from Micromechanical Finite Element Models

We demonstrate a novel strategy for the autonomous development of a machine-learning model for predicting the equivalent stress–equivalent plastic strain response of a two-phase composite calibrated to micromechanical finite element models. A unique feature of the model is that it takes a user-defined three-dimensional, two-phase microstructure along with user-defined hardening laws for each constituent phase, and outputs the equivalent stress–plastic strain response of the microstructure modeled using J2-based isotropic plasticity theory for each constituent phase. Previously, this task was addressed using linear regression approaches on a large training dataset. In this work, it is demonstrated that the use of Gaussian process regression together with a Bayesian sequential design of experiments can lead to autonomous protocols for optimal generation of the training dataset and the development of the model. It is shown that this strategy dramatically reduces the time and effort expended in generating the training set.

Effect of High-Energy Shot Peening on Surface Nanocrystallization and Integrity of AISI 4140 Steel: A Numerical and Experimental Investigation

High-energy shot peening (HESP) can introduce not only compressive residual stresses but also nanocrystalline layer close to the surface. Surface nanocrystallization leads to great improvement of surface hardness and fatigue property of treated metallic components. In this paper, a finite element method (FEM) was proposed to investigate the effects of HESP parameters, including surface coverage, shot diameter and shot velocity, on the grain refinement phenomenon. The quantitative relationship between the grain size and the equivalent plastic strain (PEEQ) was obtained by comparing the data from FEM simulation and x-ray diffraction in experiments. The surface topography and the depth profiles of microhardness and full width at half maximum were analyzed with the aim of assessing and verifying the surface integrity and nanostructure formation after HESP treatment. The results showed that appropriate increment of surface coverage, shot diameter and shot velocity was beneficial to grain refinement and nanostructure formation on a treated surface after HESP treatment. Through reasonable process control of HESP, microcracks did not appear on a treated surface even when the shot peening surface coverage reached up to 1000%.

RETRACTED: An investigation on fatigue behavior of AA2024 aluminum alloy sheets in fuselage lap joints

The purpose of this paper is to estimate the fatigue life of AA2024 aluminum alloy sheets in riveted joints under the influence of cyclic loading. First, the factors affecting the plastic equivalent strain resulting from the riveting process have been identified using the finite element method. For this purpose, a three-dimensional elastoplastic model is used for simulation. The relevant geometrical parameters such as the rivets shank length, the rivets shank diameter, and dimensional tolerances as well as pattern of where the rivets are and the material of the riveted joints are determined and subsequently the fatigue life of the aluminum joint is obtained by experimental tests. Then the fatigue life of the riveted joints is calculated using the Paris equation. To prove the validity of the analytical results, numerical modeling and experimental tests are performed on AA2024 aluminum alloy sheets in riveted joints. Numerical analysis has been performed using linear fracture mechanics and boundary element method (BEM) for the fatigue crack growth of AA2024 aluminum alloy sheets in riveted joints. Finally, the results of the analytical method for fatigue life are compared with experimental tests and numerical method that results in acceptable achievements.

Discrete-Direct Model Calibration and Uncertainty Propagation Method Confirmed on Multi-Parameter Plasticity Model Calibrated to Sparse Random Field Data

Abstract A discrete direct (DD) model calibration and uncertainty propagation approach is explained and demonstrated on a 4-parameter Johnson-Cook (J-C) strain-rate dependent material strength model for an aluminum alloy. The methodology's performance is characterized in many trials involving four random realizations of strain-rate dependent material-test data curves per trial, drawn from a large synthetic population. The J-C model is calibrated to particular combinations of the data curves to obtain calibration parameter sets which are then propagated to “Can Crush” structural model predictions to produce samples of predicted response variability. These are processed with appropriate sparse-sample uncertainty quantification (UQ) methods to estimate various statistics of response with an appropriate level of conservatism. This is tested on 16 output quantities (von Mises stresses and equivalent plastic strains) and it is shown that important statistics of the true variabilities of the 16 quantities are bounded with a high success rate that is reasonably predictable and controllable. The DD approach has several advantages over other calibration-UQ approaches like Bayesian inference for capturing and utilizing the information obtained from typically small numbers of replicate experiments in model calibration situations—especially when sparse replicate functional data are involved like force–displacement curves from material tests. The DD methodology is straightforward and efficient for calibration and propagation problems involving aleatory and epistemic uncertainties in calibration experiments, models, and procedures.

On the complete interface development of Al/Cu magnetic pulse welding via experimental characterizations and multiphysics numerical simulations

A complex Al/Cu magnetic pulse welding interface is systematically investigated using experimental characterizations and numerical simulations. A Coupled electromagnetic-mechanical simulation is proposed to compute the impact velocity and impact angle along the entire interface. This model allows to further understand the formation mechanism of various interface characteristics during MPW. The results revealed that the impact velocity gradually decreases in conjunction with the gradual increase of the impact angle. These simulations elucidate the experimentally observed successive interface morphologies, i.e., the unwelded zone, vortex zone, intermediate (IM) layers and wavy interface. Microstructural characterizations show that the IM layers are formed by mechanical mixing combined with melting and are characterized by highly heterogeneous porous zone with random sizes and distributions of void. Subsequently, an Eulerian simulation is proposed to investigate the thermomechanical effects during the wave formation which vastly influence the joint quality. The predicted wavy morphologies, temperature distribution and average equivalent plastic strain along the interface provided a better understanding on the formation steps of the experimentally observed wave morphologies. The actual kinematics during wave generation revealed that the wave was formed with repeated deformation of the interface material. The wave amplitude increases with increasing jetting angle; while the wavelength increases with increasing collision point velocity. The ratio between collision point velocity and impact velocity is found to be the most suitable parameter for explaining the influence of the collision parameters on the wavelength. These results indicate that the combination of the Coupled electromagnetic-mechanical simulation and Eulerian simulation can help us investigate the governing mechanisms of complex interface morphologies and further used to optimize the processing parameters during high speed impact welding.

Surface roughness analysis of medical grade titanium sheets formed by single point incremental forming

Single point incremental forming (SPIF) process has proven benefits in terms of formability, flexibility, and low cost as compared to conventional sheet forming, although it has some issues such as dimensional accuracy and low quality of surface finish for some materials. The SPIF is considered as a potential method of producing customised medical parts such as craniofacial implants using a titanium sheet. This investigation aims to analyse the overall surface roughness of grade 1 pure titanium along the wall of the hyperbolic truncated cone formed by the SPIF process with different forming parameters (i.e. forming tool diameter, step size, and feed rate). Focus variation microscopy was used to measure the surface roughness experimentally along the wall of the truncated cone. Abaqus/Explicit was used to predict the equivalent stress and equivalent plastic strain along the wall of the truncated cone part from the top to the fractured region to evaluate the relationship between the stress, strain, and roughness distribution. It was found that the surface roughness changes with the deformed part height and rough surface could be produced in the region of high equivalent stress and low equivalent plastic strain. Such a surface roughness and equivalent stress and plastic strain correlation has a clear implication to the design and the surface quality of sheet parts made by SPIF.

Fatigue performance prediction of Al-alloy 2024 plates in riveted joint structure

The purpose of this paper is to estimate the fatigue life of 2024 aluminum plates in riveted joints under the influence of cyclic loading. First, the factors affecting the plastic equivalent strain resulting from the riveting process have been identified using the finite element method. For this purpose, a three-dimensional elastoplastic model is used for simulation. The relevant geometrical parameters such as the rivets shank length, the rivets shank diameter, and dimensional tolerances as well as pattern of where the rivets are and the material of the rivet joints are determined and subsequently the fatigue life of the aluminum joint is obtained by experimental tests. Then the fatigue life of the riveted joints is calculated using multiple site damage (MSD). To prove the validity of the analytical results, numerical modeling and experimental tests are performed on 2024 aluminum plates in riveted joints. Numerical analysis has been performed using linear fracture mechanics and boundary element method (BEM) for the fatigue crack growth of 2024 aluminum plates in riveted joints. Finally, the results of the analytical method for fatigue life are compared with experimental tests and numerical method that results in acceptable achievements.

A Numerical Study on the Effect of Variable Wear Coefficient on Fretting Wear Characteristics.

Fretting wear is a common phenomenon that happens between contact parts when there is an oscillatory relative movement. To investigate wear characteristics history in the fretting process, the finite element method (FEM) is commonly applied to simulate the fretting by considering the wear in the model. In most literature publications, the wear coefficient is considered as a constant, which is not a real case based on the experimental results. To consider the variation of wear coefficient, a double-linear model is applied in this paper, and the tribologically transformed structure (TTS) phase is considered in the study of the wear coefficient variation model. By using these models for variable wear coefficient for both flat and cylinder, the difference of wear characteristics, plastic strain, and stress between variable wear coefficient model (VWCM) and constant wear coefficient model (CWCM) are analyzed. The results show that the variable wear coefficient has no significant effect on the wear characteristic at the end of the process in the gross sliding regime. However, in the partial slip regime, the effect of variable wear coefficient on wear characteristics is significant. Due to the difference in contact geometry in the fretting process between VWCM and CWCM, the tangential and shear stress and equivalent plastic strain also show differences during the fretting process.

Ultrasonic-assisted friction drilling process of aerospace aluminum alloy (AA7075): FEA and experimental study

Joining sheets and plates in the industry is of high importance. In the automotive and aerospace industry, using friction drilling technique is developing. In order to improve this method, different techniques have been used. In this research, applying ultrasonic vibration on the tool will be investigated. In this regard, a special tool was designed. Axial force and surface hardness were measured in friction drilling and ultrasonic assisted friction drilling. Higher rotational speed and lower feed rate induce lower axial force and higher surface hardness. In addition, ultrasonic vibration causes the surface to be harder with lower axial force. The results show that increasing the rotational speed and decreasing the feed rate in lathe machine causes axial force reduction and surface hardness increase in heat affect zone and thermomechanical region. Moreover, finite element method was carried out which indicated lower axial force occurs in ultrasonic assisted friction drilling comparing to conventional condition. Equivalent plastic strain was used to examine hardness value numerically. The obtained numerical and experiment results were in good agreement.

Experimental Evaluation of True Stress-Strain for Ductile Thermoplastics

<div class="section abstract"><div class="htmlview paragraph">Thermoplastics find application in many automotive components. Off late, hardware testing is supplemented by analysis using finite element (FE) codes. One of the factors determining the analysis accuracy is the representation of the components with suitable material models. While a uniaxial tensile test on the specimens typically provides engineering stress-strain data, material plasticity models in commercial FE solvers, such as LS-DYNA and ABAQUS, require equivalent plastic strain versus true stress as input. Engineering stress and strain can be converted to the corresponding true stress and true strain using equations based on the constant volume assumption; however, these equations are valid only up to the point of necking. A conventional approach of estimating the true stress and true strain beyond necking involves a trial and error method in which several true stress-strain curves are generated, and a finite element simulation is used to find the best possible fit with the test data. This approach is time consuming and provides an approximate true stress-strain curve beyond necking. The objective of this paper is to provide an experimental alternative to the conventional approach. Digital image correlation (DIC) was used to measure volumetric strain in the necking region of a tensile test specimen by employing two cameras simultaneously, one focusing on the front (width, length) and the other focusing on the side (thickness, length) surface of the test specimen. True strain measured by DIC in the longitudinal direction and the true stress, estimated from the applied force and measured true transverse strains, were used to generate material models for use in FE analysis without modification, i.e. without a need for correction factors. Material models were then validated by comparing the FE simulation with the tensile test results.</div></div>

Numerical study of the square cup stamping process: a stochastic analysis

The industrial demand for products with better quality and lower production costs have encouraged the widespread application of the finite element analysis (FEA) in the development and optimization of sheet metal forming processes. To ensure that the FEA solutions are reliable and robust it is important to take into account the uncertainties that inevitably arise in a real industrial environment. In this context, a numerical study on the influence of the material and process uncertainty in the stamping results of a square cup is presented. In this analysis, it is assumed uncertainty in the elasticity properties, hardening law parameters, anisotropy coefficients, blank thickness, friction coefficient and in the blank holder force. The effect of the uncertainty in these input parameters is evaluated in the punch force, equivalent plastic strain, thickness and cup geometry. Firstly, quasi-Monte Carlo method was used to evaluate the variability in the simulation outputs, considering the uncertainty of the input parameters. This analysis shows that the geometry is the output most sensitive to the uncertainty of the input parameters. Afterwards, a variance-based sensitivity analysis was carried out to identify the input parameters that most influence the output variability. It was concluded that the hardening law parameters and the anisotropy coefficients have the most influence in the stamping results variability of a square cup.

The effect of extrusion direction on the forming quality in CNC incremental forming with multidirectional adjustment of sheet posture

In the CNC incremental forming, the forming quality will be different with the different extrusion direction. The effects of the different extrusion directions on the forming quality in the CNC incremental forming with the multidirectional adjustment of sheet postures were studied by using three extrusion directions: parallel to the Z-axis, perpendicular to sheet surface and perpendicular to the surface to be formed. The algorithm for calculating the inclination angle of the extrusion tool and determining the extrusion direction vector in the multidirectional adjustment environment of sheet postures was presented. The feasibility of the algorithm was verified by an application example. The equivalent plastic strains under the three extrusion directions were analyzed through the numerical simulation. At the same time, the contour accuracy, thickness reduction and thickness distribution were compared and analyzed through the CNC incremental forming experiment with the multidirectional adjustment of sheet postures under the three extrusion directions.

Evaluation of the capacity of steel special bolted moment frame connections subjected to simulated column removal

The eight bolted stiffened extended endplate (8ES) and bolted flange plate (BFP) moment connection are two common rigid joints that are widely used in special steel moment frames (moment resisting frames with high ductility). In this study, to investigate these connections' behaviour and capacity, first, verification of finite element assumptions was carried out using the Abaqus software. Then, based on the verification models, by changing different parameters, 17 specimens were designed following the AISC Manual using two beams and three columns to determine the maximum capacity values in a column loss scenario. The finite element analysis represents that the 8ES connection's failure begins near the joint area and at the vicinity of the rib stiffener, and the BFP connections provided no warning of failure before brittle fracture of bolts at the large displacement due to catenary action mode. The plastic equivalent strain, Von-Mises stress, and middle column force–displacement curve were discussed. Finally, a formula is presented based on the numerical results to determine the displacement at the maximum capacity of these connections, a formula is presented based on the numerical results using the Least Square Method (LSM). Finally, the modification factors are presented for the theoretical formula to determine these connections' maximum capacity under column removal demands.

A high-fidelity simulation of double-sided incremental forming: Improving the accuracy by incorporating the effects of machine compliance.

Double-Sided Incremental Forming (DSIF) is a technology for the rapid, flexible manufacturing of sheet metal parts. DSIF is highly nonlinear, requiring the use of complex finite element (FE) models to optimize and control the process in order to meet geometric accuracy and sheet thinning design criteria. Current FE models do not properly take into account the effects of machine compliance, which reduces their accuracy and hinders their use for optimization and control. The aim of this work is to create a greatly improved FE model of DSIF by taking a novel approach of modeling the aggregate effects of machine and tool compliance. The accuracy of the new model was extensively validated using the local geometry, thickness distribution, principal strains, and forming forces from a funnel experiment. The validated model was used to accurately predict the spatial distribution and time-histories of the equivalent plastic strain, von Mises equivalent stress, stress triaxiality, and Lode angle parameter across and along the sheet metal. The stress state was found to rapidly change through the sheet thickness, from highly compressive between the tools and the sheet, to a mixture of generalized shear and plane strain elsewhere. Moreover, the compressive regions between the two DSIF tools created a constrained deformation zone, which likely aids in prolonging the onset of excessive thinning. This improved FE model can now be used to quantitatively characterize the nonlinear local deformation mechanisms inherent to the DSIF process, thereby providing a solid foundation for future advances in process control.

Stability Analysis of Irregular Cavities in Tunnel Using Geomagic-COMSOL Coupling Method

The erosion of soluble rock and transformation of groundwater result in the high irregularity of cavities in tunnel. At present, however, karst cavities are mainly simplified as circular, rectangular, or elliptical shape in the numerical simulation. The purpose of this paper is to propose a new method to analyze the stability of irregular cavities. First of all, we used the drilling laser scanning method to reconstruct the three-dimensional point clouds model of irregular cavities. Furthermore, we proposed the method of determining the point density to reduce the computational error under the premise of ensuring the accuracy in engineering scale. We also developed the Geomagic-COMSOL coupling numerical method to conduct the stability analysis of irregular cavities. The results demonstrated that the geometrical shape of karst cavities has great effects on the deformation and mechanical properties of the surrounding rock. The displacement and equivalent plastic strain of simplified cavities exhibited symmetric characteristics, while those of irregular cavities are highly randomly distributed. We noted that a greater displacement value and more intensive plastic strain can be triggered by irregular cavities shape, compared with the simplified cavity shape. The results also showed that the larger displacement occurred at the long-edge part, while the plastic zone was concentrated at the sharp turning angle of the irregular cavities.