Equivalent Plastic Strain Research Articles

Improved description of low-cycle fatigue behaviour of 316L steel under axial, torsional and combined loading using plastic J-integral

Low-cycle fatigue behaviour and fatigue crack kinetics of the 316L austenitic stainless steel were studied under cyclic axial, torsional and in-phase combined loading using hollow cylindrical (tubular) specimens with a small hole for crack initiation. The concept of plastic.J-integral was used, which was shown in previous studies to unify the crack growth rate data for several different materials. Dependencies of Jp on crack length were determined by extensive finite element modelling considering non-linear material behaviour according to the cyclic stress–strain curve. Locally deflected cracks were modelled in accordance with amplitudes of the axial and torsional components of combined loading. The measured crack growth rate diagrams for all types of loading and for various loading amplitudes were unified using amplitude of Jp. Fatigue lives under torsional loading were much longer than under axial loading for the same equivalent plastic strain amplitude, which was explained by higher crack driving forces in terms of Jp under axial loading than under torsional loading. Fatigue lives estimated by crack propagation based on a master curve in terms of Jp,a were in a good agreement with those obtained experimentally under all types of loading. The used concept can reduce the experimental program to obtaining of material data only for axial loading, which can then be used for prediction of behaviour under in-phase multiaxial loading. The von Mises formula for multiaxial low-cycle fatigue loading εeq,p2 = εp2 + γp2 / 3 was modified so that the fatigue lives under axial, torsional and combined loading were characterized in a matching way. Using the formula εp,Nf2 = εp2 + γp2 / 25, the fatigue life data fell on a single Coffin-Manson curve.

Numerical simulations of mixed-mode (I and II) notch tip fields in basal-textured magnesium alloys

Crystal plasticity based finite element (CPFE) simulations employing Taylor homogenization for a basal-textured Mg alloy are performed under plane strain, small scale yielding (SSY) conditions to study mixed-mode (I and II) notch tip fields. Two notch orientations are considered. In one case, the notch line and normal to the flat surfaces of the notch are taken parallel to the transverse direction (TD) and rolling direction (RD), whereas in the other, they are aligned with normal direction (ND) and TD. The results are compared against those obtained from an isotropic (von Mises) plasticity model with identical stress–strain behavior under RD tension. The maximum plastic zone size at a given level of effective stress intensity factor |K|, enhances with mode II component (i.e., with decrease in mode mixity parameter Me), and is larger for ND–TD orientation. Further, {101̄2} or tensile twinning (TT) occurs near the stretched part of the notch surface, and is more profuse as Me reduces especially for the ND–TD case. It is found that for a given Me, the notch orientation can profoundly affect the distribution of equivalent plastic strain and hydrostatic stress around the notch tip, which underscores the importance of plastic anisotropy of Mg alloys. Finally, by employing appropriate fracture criteria and the computed near-tip fields, the variations of fracture toughness and operative fracture mechanism with Me are predicted for the TD–RD case, which corroborate well with a recent experimental study.

New generation of bolted bracket connections: Safe load-carrying capacity and structural damage assessment

Double shear bolted bracket connections (DSBBs) have been introduced in 2020 as reliable, cost-efficient, fully restrained connections. The double shear performance of bolts allows efficient reduction of bolt material usage in these types of connections. This advantage also shortens the time of bolt installation in steel moment frames. The design methodology and global hysteresis response of the DSBB connections were already presented in the scientific literature. However, the present study discusses the material damage by investigating the precise stress state of DSBB segments, connection stiffness evaluation, and energy dissipation distribution around the connection. Indeed, efficiency of the design guidelines and DSBB geometrical shape is thoroughly evaluated with the help of parametric studies of this discourse. Thus, the damage investigation of the main and parametric DSBB connections is developed by monitoring the prevalent damage indices. These damage indicators are plastic equivalent strain, rupture index, longitudinal plastic strain in bolts, undesirable out-of-plane deformations, buckling deformations, and prying action. In order to validate the results of this study, Kaiser Bolted Bracket (KBB) connection as a code-prequalified connection is selected in these comparative studies. In addition to the acceptable structural performance, DSBBs have more efficient and safer performance than or at least equivalent to the code-prequalified KBB connections.

Strain-based reliability analysis of dented pipelines using a response surface method

Dent defects can decrease the life span of oil and gas pipelines. Therefore, they need constant monitoring and maintenance to ensure the pipeline’s safety and integrity. Subsequently, this paper performs a strain-based reliability analysis on pipe dent defects using a response surface method (RSM) with a quadratic response surface (RS), including the interaction terms between the RS variables. The analyses are performed to determine the factors controlling the dent defects’ probability of failure (POF). Different pipe configurations, pipe lengths, indenter sizes, and dent depths are considered in this study. A suitable finite element (FE) model for the reliability analysis was developed for this study using the FE analysis software ABAQUS. The uncertainties in the pipe wall thickness, the dent depth, the yield strength of the pipe material, and the strain capacity are considered for the reliability analysis. The first-order reliability method (FORM) is used in the RSM as the reliability method to calculate the POF and the most probable point (MPP). The POFs of several dent defects were calculated. It has been found that the POF, which is highly related to the nominal value of the maximum equivalent plastic strains generated in the dent defect, is not only related to the indentation depth or the size of the indenter. Thus, the dent depth criterion used in the engineering practice can lead to inconsistent reliability levels in dented pipes.

Dynamic Strain Aging in AA5182 Alloys at a Wide Range of Temperatures

The dynamic strain aging (DSA) on the mechanical behavior of AA5182 aluminum alloys is investigated through theoretical and numerical methods at a wide range of temperatures. This study proposes a physically-based constitutive model to explain the DSA-induced hardening of AA5182 aluminum alloys. This proposed constitutive model consists of two main components, athermal and thermal components. Between two main components, an athermal component contains an extra hardening caused by the DSA. To describe this hardening, a probability density function is introduced as a function of equivalent plastic strain, equivalent plastic strain rate, and temperature. The results show that this function can precisely describe characteristics of the DSA hardening. Experimental data obtained in the literature are utilized to examine the validity of the proposed model. Lastly, finite element (FE) solution for the proposed model is presented and validated by comparing with experimental data.

Finite element modeling of sub-surface damage while machining aluminum based metal matrix composites

Sub-surface damage during machining of aluminum-based metal matrix composites (MMCs) has been modeled using finite element models. These models are based on reinforcement particles size and volume fractions and particles are distributed uniformly in the metal matrix. In order to simulate particle debonding cohesive zone elements (CZE) have been incorporated along the parting line. In addition, failure criteria based on brittle fracture have been added for ceramic particles to simulate particle fracture. To reduce computational time and simplify the model both CZE and particle fracture is limited to the reinforced particles along the parting lines facing the tip of the cutting tool. The damage depth beneath the machined surface is measured by using the non-zero plastic strain values in the equivalent plastic strain contours obtained from the FE models. The results were compared against published experimental data and found to be in good agreement.

Influence of Crystal Plasticity Parameters on the Strain Hardening Behavior of Polycrystals

The effective mechanical properties of a polycrystal depend directly on the single-crystal properties of each grain and its crystallographic orientation with respect to the load axis. While the micromechanical approach has been used quite extensively to study the influence of grain shape and crystallographic texture on the resulting mechanical behavior of a polycrystal, the influence of the crystal plasticity parameters, which describe the constitutive behavior of the single crystal, requires to be investigated systemically because, typically, these parameters are fitted to describe a given material behavior. In the current research, this gap is filled by systemically studying the effect of changes in crystal plasticity parameters on the effective mechanical properties of polycrystals. The numerical model employed here consists of a representative volume element of 100 grains, and the material properties are described by using a non-local crystal plasticity model. A proper homogenization technique was used to homogenize the micromechanical results to an effective macroscopic material response. The equivalent stress versus equivalent plastic strain curve was obtained numerically by introducing the Voce-type hardening law, mimicking the material behavior in uniaxial tensile tests. The four parameters of the Voce-type hardening law were fitted to the macroscopic stress-strain curves, and the correlation between the crystal plasticity parameters and the Voce parameters has been studied, which is an efficient way to study the influence of microscopic material descriptions on the macroscopic behavior of polycrystals.

Investigation on the dent rebound mechanism and the structural multi-objective optimisation of sandwich pipes

ABSTRACT A thorough understanding of the denting behaviour is significant for the design of sandwich pipes. The aim of this paper is to investigate the denting behaviour of the sandwich pipe and propose a method for optimizing the cross-sectional configuration of the sandwich pipes against the denting force. The deformation process, load-displacement curve, equivalent plastic strain and energy dissipation characteristics of the sandwich pipe in the stages of dent generation and rebound are numerically examined. The subsequent parametric study shows that the hollow ratio, the thickness-to-radius ratios of the outer and inner tubes have significant impacts on the denting resistance and dent rebound performance of the sandwich pipes. The Pareto solution set for maximizing the denting resistance and minimizing the overall mass is obtained by using the non-dominated sorting genetic algorithm (NSGA-II) combined with response surface methodology. The obtained Pareto frontier is of guiding significance to the optimization design of sandwich pipes.

Energy Absorbing Properties Analysis of Layers Structure of Titanium Alloy Ti6Al4V during Dynamic Impact Loading Tests.

This paper presents the testing methodology of specimens made of layers of titanium alloy Ti6Al4V in dynamic impact loading conditions. Tests were carried out using a drop-weight impact tower. The test methodology allowed us to record parameters as displacement or force. Based on recorded data, force and absorbed energy curves during plastic deformation and sheet perforation were created. The characteristics of the fractures were also analyzed. The impact test simulation was carried out in the ABAQUS/Explicit environment. Results for one, two, and three layers of titanium alloy were compared. The increase in force required to initialize the damage and the absorbed energy during plastic deformation can be observed with an increase in the number of layers. The increase in absorbed energy is close to linear. In the simulation process, parameters such as Huber–Mises–Hencky stress value, equivalent plastic strain, temperature increase, and stress triaxiality were analyzed.

Modeling of fuel in crashworthiness study of aircraft with auxiliary fuel tank

Numerical techniques have become very practical and effective in dynamic simulation for large systems. However, till date, computational modelling of fuel in auxiliary fuel tank during aircraft fuselage section crashworthiness remains a challenge to solve. Previously, four different fluid modelling techniques, namely, Lagrange, Euler, Arbitrary Lagrange Euler (ALE) and Smoothed hydrodynamics particle (SPH) have been investigated to represent fluid in different applications ranging from marine science to rotorcraft fuel tank crashworthiness. However, for a full-scale aircraft fuselage section with auxiliary fuel tank, fluid modelling has not been yet reported. Therefore, in this current research, a commercial explicit dynamic code Autodyn is adopted to solve Fluid-structure interaction (FSI) problems numerically on a standalone civil aircraft type fuel tank with four different fluid models, respectively, i.e. Lagrange, Euler, Arbitrary Lagrange Euler and Smoothed Hydrodynamics Particle. Virtual drop tests are conducted with a vertical impact velocity of 7 m/s to investigate the most suitable fluid model, which can be further utilized to represent fuel inside an auxiliary fuel tank in a fuselage section to study the crashworthiness. After studying the structural deformation, von Mises stress, equivalent plastic strain, absorbed internal energy, fluid sloshing events and computational time duration due to the adoption of different fluid models, it is found that Lagrange fluid model with the node erosion algorithm setup suits best to the fuel. In the second part of the research, crashworthiness of a full-scale fuselage section with auxiliary fuel tank considering fluid as Lagrange model and fluid as distributed mass is investigated. Results are compared with the available experimental and numerical outcomes and it is found that, modeling the fluid inside of an auxiliary fuel tank is crucial to capture the appropriate plastic deformation of the fuselage section; however, presence of fluid does not affect the acceleration responses of the cabin floor.

Probing the effect of surface parameters and particle size in the diffusion-induced stress of electrodes during lithium insertion

Experimental studies have shown that the active particles of electrodes undergo phase transformations during ion-insertion, which are accompanied by diffusion induced stresses that result in fracture at the particle surface. Only a few studies have considered the effect that the surface stress has on the diffusion-induced stress that occurs in electrode materials that undergo elastic deformations during ion-insertion, while no studies have accounted for the effect of surface stresses in the case when plastic deformation is also present. In addition, there are only few comprehensive studies on the competing effect between the surface stress and the strain gradient during ion diffusion. The present work sheds light on the effect that the particle size has on the stresses generated due to the phase transformations that take place during ion-insertion by accounting for the surface residual stress with strain gradient elasticity or strain gradient plasticity. Due to the presence of surface stresses, the stress on the particle outer surface can be significantly reduced. In particular, when the residual surface stress and the surface elastic modulus are both positive, the hoop stress at the outer surface remains compressive, whereas tensile stresses are required for crack formation. This work, therefore, indicates that surface modification could be an effective approach for improving the structural integrity of electrodes during the lithiation process. The additional consideration of strain gradients further reduces the value of the equivalent plastic strain for elasto-plastic electrode particles. These findings render prospective insights for designing next-generation mechanically stable phase transforming electrode materials.

Force Controlled Low Cycle Fatigue (LCF) Life Evaluation Methodology Based on Unstabilized Material Properties

Low Cycle Fatigue (LCF) is a prominent failure mechanism in many design components; therefore, an evaluation of cycles to failure in this regime is of high importance. Most international standards recommend a closed loop strain-controlled mode specimen testing in this regime. However, the ꜪN data obtained from this test is not suitable for life evaluation of parts enduring force-controlled history during actual service without correction for control mode. Many existing procedures, which accounts for cyclic strain stabilization during force-controlled loading may significantly complicate the finite elements analysis (FEA) at solving or post processing stages and are often an inherent source of uncertainty. A heuristic, cost effective and sufficiently accurate approach for LCF life estimation is advocated. The method involves only two force loading FEA simulations, one of the actual parts and the other of the test specimen, using initial unstabilized stress strain curve, followed by a limited number of force-controlled specimens testing. Actual part and specimen life correlation performed using first loading unstabilized equivalent plastic strain value Ꜫp1 under locality and similitude assumptions. Unstabilized strain vs. number of cycles to failure curve Ꜫp1N is constructed and discussion regarding specimen geometry considerations for providing sufficient accuracy is included. Method validation and crack propagation study are provided.

Fatigue behaviour of dental implant using finite element method

An attempt has been made in this study by employing the Deshpande and Fleck constitutive model, which is available in the ABAQUS software as the crushable foam material model, to reflect the stress-strain behavior of dental implants made of titanium foam (Ti-foam) under fatigue loading. For comparison purposes, solid Ti has also been considered in the study. Before proceeding to the study of fatigue loading effect on the implant, the modelling approach has been tested with the results of a compression test available in the open literature. Equivalent plastic strain, effective stress, and hydrostatic stress qualities have been generated for various porosity levels. Fatigue loadings corresponding to all three directions namely, lingual, axial, and mesio-distal directions have been applied on the implant for 50 load cycles in order to observe the fatigue loading effect on the implant. It has been observed from the simulation results that under identical conditions, stress generated in the Ti-foam material is less and Ti-foam can also transfer more loads to the surrounding bones as compared to the correspondings of solid Ti material. Therefore, Ti-foam based implant can solve the stress shielding effect and hence Ti-foam is a suitable alternative of the solid Ti for fabricating dental implants.

Investigation of the effects of shot overlap and rigid body assumptions on surface layer characteristics in shot peening simulation

As an important mean of shot peening (SP) research, finite element simulation has been widely and successfully employed in estimating the surface characteristic and residual stress distribution after SP treatment. In this study, the effects of shot overlap and rigid body assumptions on dimple geometry and residual stress distribution in depth were discussed via the validated ordered dimple pattern and stochastic dimple pattern SP models for quenched and tempered 42CrMo steel. The results show that shot overlap assumption has a great influence on the surface plastic deformation of peened material. The simulated value of plastic deformation is much larger than the experimental value, which results in the residual stress of the overlapping shot SP model deviating from the actual result seriously. For the prediction of the residual stress distribution, the shot must be set as an elasto-plastic body when the number of shot is large. The shot can be set as a rigid body for the aim of reducing the calculation time when the number of shots is small. In addition, the influence of material hardness on residual stress and equivalent plastic strain (PEEQ) was investigated via simulating the residual stress and PEEQ of different hardness materials treated by SP process . • It is necessary to choose the non-overlapping shot in SP simulation when the dimple geometry and residual stress distribution is predicted. • It is more accurate to choose elasto-plastic shot in SP model for the dimple geometry prediction. • The shot can be set as a rigid body when the number of shot is small.

Analysing the Performance of Hollow Core Slabs Strengthened with CFRP

External bonding with CFRP (Carbon Fiber Reinforced Polymers) has been investigated over the last decade, as it represents a viable technique of strengthening existing prestressed concrete structures, including hollow-core slabs (HCS) with non-circular voids. The high performance of these carbon fibers has been validated through a large volume of experimental and numerical research and yet there are a few issues which remain controversial in simulating their behaviour with the finite element modelling. Although the CFRP mechanical properties are provided by the manufacturers, they are not satisfactory for a complete understanding of the analysis and design approach of HCS strengthened with CFRP. The present research is conducted on prestressed HCS with non-circular voids. The strengthening method consisted in the application of the composite material on the slab’s end internal regions of the voids, on a 500mm length: 1 layer and 2 layers. The objective of this study is to emphasize the effect of damage in the CFRP strips and moreover the interface effectiveness on the CFRP strengthened HCS. Damage is predicted using Hashin’s initiation criteria and the cohesive behaviour in the interface is used to analyse the epoxy resin which bonds the CFRP sheets to the hollow-core units. A plastic damage model was used for modelling the concrete, after a parametric study regarding the dilatancy angle and viscosity parameter was conducted for the most appropriate choice of concrete damage plasticity parameters. The overall procedure consists of numerical FE modelling in Abaqus software. Two different modelling possibilities of CFRP-to-concrete interface were studied: a tie constraint connection was first used and secondly the contact bonding was defined with the cohesive behaviour option of the contact interaction property. The results are provided in terms of load-displacement response, equivalent plastic strain and distribution of Von Misses stresses in the CFRP strips.

Effect of localized defects on mechanical and creep properties for pyramidal lattice truss panel structure by analytical, experimental and finite element methods

The localized defects, including the ruptured truss and debonding joint, have been severely threatening the structural integrity of the pyramidal lattice truss panel structure (PLTPS). In this paper, a series of analytical models, i.e., equivalent elastic modulus, plastic and creep strain rate models, were developed to study the effects of localized defects on the mechanical properties and creep performance of the PLTPS, which have been verified by the experiments and finite element (FE) simulation. Based on the experimental data, the equivalent elastic modulus model was modified when the defect fraction exceeds the threshold value. The complete stress–strain curve was plotted by the proposed analytical models. At elevated temperature, both the analytical model and finite element results indicate that the equivalent creep rate increases exponentially with the increase of the defect fraction. In addition, for the long-term service, the total equivalent strain is the superposition of the steady-state creep strain and the saltatorial strain stimulated by the inconsecutive stress once the truss or joint fails, which is more susceptible to the effective stress comparing with the servicing time. The proposed analytical model which considering the effect of localized defects of the PLTPS provides an efficient criterion to justify whether the structure with certain defects satisfies the engineering requirements.

Two novel corrugated web reduced beam section connections for steel moment frames

In a new type of Reduced Beam Section (RBS) connection, called the corrugated web RBS connection, the flat web of the beam in the section near the column face is replaced by corrugated plates so as to reduce the flexural strength of the beam and ensure hinge formation in this section. The use of the corrugated web in the reduced section zone increases the lateral-torsional stability of the beam and reduces its flange width-to-thickness ratio. This paper presents two new types of corrugated web RBS connection, called the curved cell web RBS (CW-RBS) and the hexagonal cell web RBS (HW-RBS). The design method is described and the seismic behavior of the connections is evaluated through finite element modeling and analysis. After validating the numerical model with the existing experimental data, a number of models created with the proposed details but for different beam and column sections and by considering three different depths for the corrugated cells are analyzed under cyclic loading. A number of control models including the radius cut RBS (RC-RBS), the accordion web RBS (AW-RBS), and the tubular web RBS (TW-RBS) connections are used for comparison. The results show that the proposed connections cause plastic hinges to emerge in the RBS zone, thereby preventing failure at the beam-column junction. The proposed connections offer stable hysteretic behavior with better ductility and lower strength degradation than the conventional RC-RBS connection. The proposed connections also develop significantly lower maximum equivalent plastic strains than both AW-RBS and TW-RBS, which can delay the failure of the beam in the RBS zone. • Introduction of two new corrugated web RBS connections for steel moment frames. • Providing a simple method for flexural and shear design of the proposed connections. • The proposed connections exhibit stable hysteretic behavior with high ductility. • The proposed connections offer better seismic performance and energy dissipation than conventional RBS connections.

Wavelet Packet Method for Locating Critical Slip Surface Using the Strength Reduction Method

When the finite element-strength reduction method is used for two-dimensional slope stability analysis for elastic-perfectly plastic material, the failure criterion usually adopts the criterion of plastic zone penetration. That is, when the slope is in the limit equilibrium state, the plastic zone goes through the slope from the toe to the top. Meanwhile, the critical slip surface is composed of a series of points of maximum equivalent plastic strain along the depth direction. By deploying a set of parallel lines approximately perpendicular to the slope surface and picking out the points of these lines with the maximum equivalent strain points, we obtain a series of points taking on a wave shape, which constitutes a signal function. Subsequently, the wavelet packet analysis is used to smooth these points, i.e., locating the critical slip surface. The analysis of classic examples and comparison with Spencer’s method show that the proposed method in this paper is reasonable and effective.

A dual-scale FE simulation of hole expansion test considering pre-damage from punching process

The effect of the hole-edge condition on the hole-expansion ratio (HER) of ferrite-bainite (FB) dual-phase steel is analyzed by developing a dual-scale finite element (FE) approach. The proposed dual-scale approach consists of macroscale simulation of hole expansion test (HET) and microscale simulation for capturing localized inhomogeneous deformation at the microstructure level. The macroscale HET simulation considers the experimentally measured hole-edge geometry and hardness profile under different clearance conditions. The deformation history in the region of interest calculated from the macroscale simulation was transferred to the microscale simulation as boundary conditions. In the microscale simulation, the deformation inhomogeneity within the two-phase microstructure was calculated by considering the dislocation pile-up at the grain boundaries. In the experimental aspect, the geometry and surface roughness of the hole edge, which are factors for quantifying the damage from the punching process, were measured using a confocal microscope. The work hardening of the material was quantitatively analyzed by measuring the hardness profile in the radial direction from the hole edge. For the work hardening due to the punching process, the measured hardness is converted into an equivalent plastic strain, which is transferred to both macro-and microscale models in the form of pre-strain. The predicted HERs are compared with the experimentally measured HER values, and it is confirmed that the damage caused by punching is critical to the hole expansion formability of the dual-phase FB steel.

A modified friction model and its application in finite-element analysis of friction stir welding process

The application of the Eulerian based computational solid mechanic (CSM) models in numerical modeling of friction stir welding (FSW) is not deeply studied, because implementing a complicated friction model in an Eulerian based CSM model is challenging. To overcome this, the literature used Eulerian based computational fluid dynamics (CFD) models. On the other hand, due to the usage of finite element methods (FEMs) instead of finite volume methods (FVMs), the accuracy of CSM is higher than CFD. In this paper, for the first time, a modified friction model is implemented in an Eulerian based CSM model. To investigate the influence of the friction model on the stress, material flow, equivalent plastic strain and temperature, a comparison between the modified friction model and the Coulomb friction model is done. Developing the modified friction model results in achieving four phases for the relationship between the relative velocity and ratio between the shear stress and pressure. The comparisons of FE models show that, the modified friction model has been successful in simulating the partial sliding/sticking condition, because of achieving a uniform pattern for the stress with the maximum values of 150 MPa. Moreover, a successful prediction the material flow, heat flux, equivalent plastic strain and temperature is also obtained. Maximum values of the equivalent plastic strain is found to be 14. A “M” shape form, shifted to the advancing side with the peak temperature of 413 °C (5 mm far from the welding center) is also found. Finally, the results of the model in which the modified friction model is employed are found to be in correlation with experiments and the literature.