Equivalent Plastic Strain Research Articles

Surface hardening analysis for shot peened GH4720Li superalloy using a DEM-FEM coupling RV simulation method

A systematic study was performed to analyze the surface hardening of shot-peened GH4720Li superalloy by combining experiments and numerical simulations. Firstly, it was proved that fine grain strengthening (FGS) and work hardening (WH) are two main strengthening mechanisms of the hardened layer for the plate specimen after shot peening (SP). Then, in order to improve the simulation efficiency, a coupled discrete element method-finite element method model (DEM-FEM) was integrated into the representative volume model to obtain strength distribution quantitatively. The simulation of grain refinement was realized through the dislocation density evolution equation and the degree of WH was characterized by the equivalent plastic strain. Motived by the Vickers hardness test principle, a novel expression between strength and hardness was finally deduced considering both WH and FGS mechanisms, based on which the hardness distribution was evaluated after SP treatment. The hardness by the numerical framework revealed a good agreement with the experimental observations.

Study on Fracture Parameters of Stress Corrosion Cracking Tip of AA6082 Alloy at the Microscopic Scale

A two-dimensional finite element model is used to explore the fracture parameter in the tip region of stress corrosion crack (SCC) of AA6082 alloy. Based on the ABAQUS code, we investigate the effect of oxide film’s yield stress on the Mises stress and equivalent plastic strain (PEEQ) in the crack tip. The results show that as the yield strength of oxide film increases, the Mises stress and PEEQ of base alloy in crack tip area both decrease, and the stress of oxide film in crack tip also reduces, but the strain increases. This is because the oxide film bears more load, so the load on the base alloy of the crack tip becomes smaller, resulting in a reduction in the stress and strain on the base.

Numerical studies on laser impact welding: Smooth particle hydrodynamics (SPH), Eulerian, and SPH-Lagrange

Smooth particle hydrodynamics (SPH) and Eulerian methods are widely used in the numerical simulation of laser impact welding (LIW). However, SPH method cannot directly apply pressure load generated by plasma and can only realize the loading effect of the plasma pressure load by presetting the shape and initial velocity of the flyer plate. However, the welding interface waveform and jet phenomenon produced by the Eulerian method due to the regular material mixing mode is not as clear as that by the SPH method. In addition, it cannot effectively show the central springback and cracking in the LIW. A new numerical simulation method for LIW, namely, smooth particle hydrodynamics and Lagrange coupling method (SPH-Lagrange). The idea is to couple the Lagrange grid and SPH particles on the flyer model, which can apply the impact load generated by the plasma on the upper surface of the flyer model; as a result, the loading conditions are in line with reality. The simulation results of local velocity, shear stress, equivalent plastic strain, and temperature state of the welding interface obtained by the SPH, Eulerian, and SPH-Lagrange methods were compared and studied. The interface waveforms obtained by different laser energies were compared with the simulation results of the SPH-Lagrange method. The numerical simulation calculations show that the SPH-Lagrange method is more consistent with the LIW experiment. Compared with other methods, SPH-Lagrange method is more suitable for the simulation of the LIW combination process and interface characteristics. Finally, the possible existence of melting phenomenon in LIW process was investigated using the SPH-Lagrange method.

Shaking table test study on seismic performance of UHPC rectangular hollow bridge pier

To study the seismic failure mode and dynamic response characteristics of ultra-high performance concrete (UHPC) rectangular hollow bridge pier under dynamic loads, the El Centro wave, Taft wave, and Northridge wave were selected as seismic excitation for the shaking table test. The responses such as natural frequency, damping ratio, acceleration-time and displacement–time curves were investigated and the results were compared with the finite element simulation results. At the same time, 8 finite element models (FEMs) of UHPC rectangular hollow bridge pier were established to explore the influence of longitudinal reinforcement ratio and stirrup ratio on the seismic performance of bridge piers. The results indicated that with the increase of peak ground acceleration (PGA), the damping ratio, acceleration, displacement and UHPC strain of the specimen increased, while the natural frequency and the dynamic amplification factor of the pier decreased gradually due to the accumulation of damage. The increase of longitudinal reinforcement ratio improves the ductility, and the increase of stirrup ratio enhances the constraint effect of core UHPC and ductility to a great extent, which leads to different acceleration, displacement and equivalent plastic strain response of bridge piers. On the whole, the stiffness of UHPC rectangular hollow bridge pier was degraded after the input of seismic wave, but the ultimate bearing capacity was not deteriorated. The overall seismic performance is superior. In areas with low seismic fortification intensity, the reinforcement ratio of UHPC rectangular hollow bridge piers can be appropriately reduced.

Ultimate capacity and failure mechanism of SCS and S-UHPC composite deep beams: Test and modeling

In this study, a type of steel–concrete–steel (SCS) composite deep beam with ultra-high-performance concrete, named S-UHPC deep beam, was developed. Eight simply supported deep beams, including three SCS deep beams and five S-UHPC deep beams, were tested under static loads. The effects of different parameters (including the shear span ratio, concrete type, and shear stud spacing) on the ultimate capacity, ductility, and interfacial slip of the specimens were explored. Moreover, the observed failure modes were categorized into shear failure without slip, slip failure, and flexural failure with the snapping of steel fibers. To analyze the failure mechanism systematically, finite element (FE) models of the specimens were established and validated. By analyzing the FE simulation results on the compressive damage and stress distribution of the filled concrete, the von Mises stress distribution of shear studs, and the equivalent plastic strain distribution of the bottom steel faceplate, the failure mechanism of the specimens with the observed failure modes was simplified as a modified Strut-and-Tie model. Based on the force transfer analysis of the modified Strut-and-Tie model, a slip coefficient was deduced to quantify the composite action and provide theoretical supports for the reasonable design of shear connectors. Theoretical models of SCS deep beams and S-UHPC deep beams with different failure modes were presented to predict the ultimate capacity.

Initial cyclic hardening behavior of cracked structures under large-amplitude cyclic loading

A new cyclic hardening model is proposed based on combined experimental and numerical analyses to simulate the deformation of a cracked structure under large amplitude cyclic loading. In the experiment conducted herein, compact tension specimen tests made of TP304 stainless steel were subjected to large-amplitude cyclic loading. Then, finite element (FE) analysis was performed using the ABAQUS debond option to develop a cyclic hardening model. In the proposed cyclic hardening law, isotropic hardening was calculated in the first loading cycle. To assess the unloading of the first cycle, a Chaboche combined hardening model was used. The model results agreed well with the experimental displacement data. The effects of hardening in the first loading cycle on the yield surface and equivalent plastic strains in the subsequent cycles are presented as well.

Experimental study on the seismic behavior of a new single-faced superposed shear wall with the concealed column

To better meet the requirements of building industrialization, this study proposes the use of a concealed column to connect the two single-faced superposed shear walls horizontally. The seismic behavior, such as failure mode, hysteresis loop, skeleton curve, ductility coefficient, and reinforcement strain, of the single-faced superposed shear wall is studied using the pseudo-static test method, with the integral cast-in-place shear wall under the same geometric dimensions and experimental conditions as the control group. The research results show that the seismic behavior indexes of the two specimens are close under 0.1 axial compression ratio, indicating that the new specimen can be equivalent to cast-in-place, which possesses better overall mechanical performance and excellent seismic behavior. The vertical seam structure with the concealed column is reasonable; thus, the prefabricated and the cast-in-place parts in the new single-faced superposed shear wall can work together to withstand external loads. Finally, ABAQUS finite element analysis is carried out on the new single-sided superposed shear wall specimen and cast-in-place shear wall specimen. The analysis results of the concrete equivalent plastic strain nephogram and the reinforcement Mises cloud diagram are consistent with the test results; the trends of the hysteresis loop and skeleton curves are basically similar.

Rate-dependent strength and ductility of binder jetting 3D-printed stainless steel 316L: Experiments and modeling

Binder-jetting is an additive manufacturing process for metals which involves the rapid making of a binder bonded metal powder part followed by the removal of the binder and creation of a fully dense part in a subsequent sintering step. This emerging process has the potential of high cost efficiency as compared to selective laser melting (SLM) or shaped metal deposition. Here, we determine the rate-dependent plasticity and fracture properties of binder-jetted stainless steel 316L. Electron Back-Scattered Diffraction (EBSD) analysis and tomography revealed an equi-axed grain structure with an initial porosity of 3%. The latter is due to pores with an average size of 20μm that are clustered in layers perpendicular to the build direction. The observed stress-strain curve of the binder-jetted material always lies below that of wrought stainless steel 316L with a 50% lower initial yield stress and a 30% lower ultimate strength. Both the material anisotropy and strain rate sensitivity may be considered as second order effects in that comparison. The equivalent plastic strain obtained from fracture experiments for different stress states is also always lower for the binder-jetted material. The observations for the binder-jetted material therefore stand in stark contrast to those for SLM-made stainless steel which can provide an even higher yield strength than the wrought material. From a mechanism point of view, the low mechanical properties of the binder-jetted material may be explained by the high initial porosity which is reminiscent of cast metals.

Round robin analysis to investigate sensitivity of analysis results to finite element elastic-plastic analysis variables for nuclear safety class 1 components under severe seismic load

As a part of round robin analysis to develop a finite element elastic-plastic seismic analysis procedure for nuclear safety class 1 components, a series of parametric analyses was carried out on the simulated pressurizer surge line system model to investigate sensitivity of the analysis results to finite element analysis variables. The analysis on the surge line system model considered dynamic effect due to the seismic load corresponding to PGA 0.6 g and elastic-plastic material behavior based on the Chaboche combined hardening model. From the parametric analysis results, it was found that strains such as accumulated equivalent plastic strain and equivalent plastic strain are more sensitive to the analysis variables than von Mises effect stress. The parametric analysis results also identified that finite element density and ovalization option in the elbow elements have more significant effect on the analysis results than the other variables.

Evaluation of heterogeneous mechanical tests for model calibration of sheet metals

The accuracy of strategies combining heterogeneous mechanical tests and full-field strain measurement techniques is dependent on many factors. Recently, many heterogeneous mechanical tests with different specimen shapes have been proposed using optimization techniques or empirical knowledge. However, a comparison of heterogeneous mechanical tests is a difficult task because studies use different materials and different representations of the strain and stress states. This work discusses metrics, calculated from the stress and strain tensors, to evaluate heterogeneous mechanical tests and proposes a metric to evaluate the tests’ sensitivity to anisotropy. To illustrate the approach, four heterogeneous mechanical tests are evaluated through the use of the suggested metrics. Results show that the use of various metrics provides a good basis to evaluate heterogeneous mechanical tests. Moreover, this work identifies a heterogeneous mechanical test achieving a high range of mechanical states and high values of equivalent plastic strain.

On fracture locus of corroded steel plates with nominal fracture strain and corrosion morphology

In order to study the fracture ductility of corroded steel plates under tension load, a series of tensile tests and numerical calculations on corroded steel plates were conducted. The results showed that corrosion damage would increase the speed of equivalent plastic strain growing at critical point, and decrease the equivalent plastic strain to fracture, thus degrade the nominal strain at fracture. The weakened and uneven cross-section along longitudinal direction caused by corrosion damage led to the strain concentration and accelerated growth of equivalent plastic strain. The corrosion pits increased the values of stress triaxiality and Lode stress parameter, thus degenerated the equivalent plastic strain to fracture. Based on the above results, the fracture locus of corroded steel plates in the nominal strain to fracture-corroded morphology space was established.

Stability Analysis of Underground Pillar Supporting System under Different Disturbed Stresses

Small external disturbances may destabilize the bearing pillar, which in turn will change the stress distribution of the pillar supporting system, leading to its overall instability. Based on the engineering background of a mine and the mechanical analysis of pillar under disturbed stress, this paper investigated the stress, strain, and plastic zone of the pillar supporting system under different disturbed stresses. Then, the chain instability of the pillar supporting system was achieved. The law of stress transfer and plastic development of the pillar supporting system was explored. The results showed that the greater the disturbed stress, the faster the increase rate of the maximum stress of the pillar supporting system. As the width of the pillar increased, the maximum stress of the pillar decreased, so its risk of damage decreased. As the disturbed stress increased, the maximum principal strain and equivalent plastic strain of the 6 m wide pillar increased approximately linearly, and their growth rates of the 4 m wide pillar gradually increased. In the process of chain instability of the pillar supporting system, the sides of the middle pillar were destroyed first, and then the plastic zone gradually penetrated, causing the stress of the adjacent pillar to increase, which in turn led to its destruction. By analyzing the monitoring data of stress, displacement, or plastic strain, the instability of the pillar can be predicted.

A numerical Approach to design and develop freestanding porous structures through cold spray multi-material deposition

Cold spray is a solid-state particle deposition technique with a wide range of applications for coating, repair and additive manufacturing. Cold spray parameters are normally tuned to obtain deposits with minimal porosity and thus highest strength. However, there are specific applications such as biomedical prostheses, heat sinks and energy absorbing products, where a higher exposed surface area can lead to enhanced performance, rendering porosity a desirable feature. Few recent studies have experimentally evaluated the potential of cold spray technology for obtaining porous deposits. To enhance the efficiency of these approaches, here we developed a detailed numerical framework that can determine the topological and mechanical features of cold spray porous deposits. A series of combined Eulerian-Lagrangian finite element models were developed considering a multi-material feedstock, one constituent of which served as a porogen. Different powder blends of pure Ti mixed with either Al or Cu, as the sacrificial powder, with varying volumetric fractions were analysed. A novel post-processing approach was developed to remove the sacrificial powder and extract distinct characteristic indicators from the simulations' output; these indices include porosity and structural connectivity of the remaining Ti structure. Equivalent plastic strain was considered as an index to assess the strength of the resultant deposit. The obtained data regarding particle deformation were in agreement with preliminary experimental tests. The numerical results revealed that Ti-Cu combinations can yield deposits with higher Ti particle deformation compared to the Ti-Al blend and hence, lead to a better inter-particle bonding. This study presents a robust numerical approach for selection of cold spray process parameters towards obtaining coatings and freestanding porous metal parts with modulated porosity, connectivity and strength.

Strain response analysis of API 5L X80 pipelines with a constrained dent subjected to internal pressure

Constrained dents normally cause serious plastification on the pipe under internal pressure due to the restraint of the indenter. Therefore, in this work, the strain response of the API 5 L X80 (referred to as X80 in the remainder part) steel pipeline containing a constrained dent was investigated. Firstly, the formation process of the constrained dented pipeline was numerically simulated by establishing a 3D finite element (FE) model. The model was then verified against the test results of other researchers. The validated model was employed to investigate the equivalent plastic strain distributions of the constrained dent created during the pipe construction and pipe operation stages. Finally, an extensive parametric study was conducted to examine the effects of the internal pressure, dent depth, diameter-to-thickness ratio, indenter size and shape on the strain response of the constrained dented pipe in detail. The results show that the maximum equivalent strain of shallow dents locates at the pipe inner wall at the dent center. As the dent depth increases, the maximum strain position deviates from the dent center and moves outwards along the pipe circumferential direction. Compared with the constrained dent formed during the pipe construction period, the maximum equivalent strain of the in-service constrained dented pipelines is larger under the identical dent depth. The maximum strain increases significantly as increasing the dent depth and internal pressure. It is noted that the wall thickness has a greater influence on the equivalent plastic strain distributions of the constrained dented pipe than that of the pipe diameter. The equivalent plastic strain caused by a small indenter is more serious than the large one due to the high strain concentration. It is noteworthy that circumferential dent (dent length is less than dent width) can be considered as the most severe form of dent defects on the pipe in comparison to the axial dent (dent length is greater than dent width) and dome dent (dent length is approximately equal to dent width).

A variational phase-field model For ductile fracture with coalescence dissipation

A novel phase-field model for ductile fracture is presented. The model is developed within a consistent variational framework in the context of finite-deformation kinematics. A novel coalescence dissipation introduces a new coupling mechanism between plasticity and fracture by degrading the fracture toughness as the equivalent plastic strain increases. The proposed model is compared with a recent alternative where plasticity and fracture are strongly coupled. Several representative numerical examples motivate specific modeling choices. In particular, a linear crack geometric function provides an “unperturbed” ductile response prior to crack initiation, and Lorentz-type degradation functions ensure that the critical fracture strength remains independent of the phase-field regularization length. In addition, the response of the model is demonstrated to converge with a vanishing phase-field regularization length. The model is then applied to calibrate and simulate a three-point bending experiment of an aluminum alloy specimen with a complex geometry. The effect of the proposed coalescence dissipation coupling on simulations of the experiment is first investigated in a two-dimensional plane strain setting. The calibrated model is then applied to a three-dimensional calculation, where the calculated load-deflection curves and the crack trajectory show excellent agreement with experimental observations. Finally, the model is applied to simulate crack nucleation and growth in a specimen from a recent Sandia Fracture Challenge.

Multi-dimensional mechanical response of multiple longitudinally aligned dents on pipelines and its effect on pipe integrity

Dents have been identified as among the most common deformation defects in oil and gas pipelines. In this study, the multidimensional mechanical responses, springback, and rerounding behaviors of dents as well as the interaction of multiple dents on pipelines and their effect on pipe integrity were investigated through the three-dimensional finite element method and full-scale burst tests. The burst test demonstrates that a plain dent has a minimal effect on the pipeline burst pressure, and the burst failure position is not located in the dented area. Generally, when a dented pipeline that is subjected to monotonically increasing internal pressure bursts, the dent does not fully reround, and a convex protuberance forms in the axial shoulders on both sides of the dent. During pressurization, the maximum equivalent plastic strain in the dented pipe always occurs on the inner surface near the dent center in which no necking is found in the radial direction of the wall thickness. However, a larger equivalent stress is observed around the edge of the dent center, whereas the stress at the center is relatively small, resulting in the formation of a plastic hinge in the dented area. If internal pressure fluctuations occur, this can easily lead to fatigue failure. Finally, the interaction among multiple longitudinally aligned dents was investigated, and the critical spacing affecting the integrity of the pipeline was determined. The investigation reveals that when the dent spacing exceeds the pipe diameter, the interaction between two dents may be ignored, and the dent effect on the pipe integrity may be separately evaluated. However, if the dent spacing is less than 0.5 times the pipe diameter, then the dents must be treated as a combined dent. Further, if the spacing is 0.5–1.0 times the pipe diameter, then dent interaction must be considered.

Multi-Pass Welding Distortion Analysis Using Layered Shell Elements Based on Inherent Strain

In this article, a layered shell element-based, elastic finite element method for predicting welding distortion in multi-pass welding is developed. The welding distortion generated in each pass can be predicted by employing layer-by-layer equivalent plastic strains as thermal expansion coefficients and using the heat-affected zone (HAZ) width as the mesh size. The final distortion can be expressed as the sum of the distortions for each pass. This study focuses on extraction of the equivalent plastic strain and HAZ width through 3D thermal elastic plastic analysis (TEPA) for each pass. The input variables extracted from each pass can be converted and added to simulate the final distortion of the multi-pass welding. A 10 mm thick, multi-pass butt-welded joint, subjected to three passes, is simulated via the proposed method. The predicted welding distortion is compared with the 3D TEPA results and the measured experimental data. The outcome indicates that good agreement can be obtained.

The Effects of Piercing Methods on Burring Formability under Practical Hole Diameter

Advanced High Strength Steels (AHSS) sheets are used for automobile bodies to comply with the demands for weight reduction and collision performance. However, as the tensile strength is increasing, the ductility of steel sheets is decreasing. Therefore the forming defects such as fractures may occur. In case of chassis components, it is needed to prevent stretch flange fractures from burring edge. There are following methods to improve burring formability. 1) Double Punching Method (DPM): punching blank coaxially with a pre-punched hole. 2) Humped bottom Punch Method (HPM): punching blank under tension using a punch with a humped part. However, there isn’t much previous evidence evaluating the burring formability of DPM and HPM under practical punching diameter for chassis components. In this study, the burring formability using DPM and HPM has been evaluated under 30mm punching diameters, through experiments and FEM analysis. The results showed that: 1) DPM: deforming mainly occurred in scrap side and equivalent plastic strain was reduced on the punched edge surface. 2) HPM: the burring formability requires both increasing stress triaxiality in blank and reducing equivalent plastic strain applied by the preceding bumped part. Under identical conditions, the same improvement effect of DPM was obtained with HPM.

Unified correlation of constraints with crack arrest toughness for high-grade pipeline steel

There is much controversy surrounding using laboratory specimens to predict the fracture behavior of high-grade pipeline steel due to their different constraints. Since there is a lack of unified parameters to quantitatively characterize the constraint effects, a model for the transformation of crack arrest toughness between different specimens and pipes has not been formed. In order to solve this problem, the evolution law of the plastic zone of the crack tip with the crack tip opening degree under different in-plane and out-of-plane constraints is explored using the finite element simulation technology. On this basis, a constraint parameter η which is based on the area APEEQ surrounded by the isoline of equivalent plastic strain εp at the crack tip is proposed. The feasibility of this parameter to characterize both in-plane and out-of-plane constraints is discussed, and a quantitative correlation model between it and the crack arrest toughness, critical crack tip opening angle (CTOAC), is established. The results show that the proposed parameter can be used to characterize the overall constraints caused by different specimens with different loading forms and geometries. The normalized arrest toughness, CTOAC/CTOAref, has a linear relationship with η1/2, and the correlation line is only related to the material. The quantitative correlation model has universal applicability for different specimens and is expected to predict the transformation of crack arrest toughness between laboratory specimens and pipelines.

Numerical study on the collision of Platform Supply Vessel and Floating Production Storage and Offloading platform

ABSTRACT The first Floating Production Storage and Offloading platforms (FPSOs), many still operating in Campos Basin, were converted from single-hull oil tankers. Therefore, collision leading to the FPSO side plating fracture is a serious concern. To simplify the numerical simulation of collision a Platform Supply Vessel (PSV) is modelled assuming a perfectly rigid bow structure, which can deem excessively conservative assessment. Therefore, the objective of this paper is to evaluate the actual expected collision damage considering a deformable PSV bow structure. In this investigation, the resistance of a single-hull FPSO side structure is studied for two collision scenarios, considering the PSV bow rigid and deformable and employing RTCL and plastic strain fracture criteria. It is shown that the conservative combination of equivalent plastic strain criterion and rigid bow may overestimate the damage severity, while the consideration of deformable PSV bow and RTCL criterion does not lead to a single-hull FPSO fracture for the collision scenarios investigated.