Effective Plastic Strain Research Articles

Effects of heterogeneous plastic strain on hydrogen-induced cracking of twinning-induced plasticity steel: A quantitative approach

Heterogeneous plastic strain is essential for understanding hydrogen-induced crack (HIC) initiation in twining-induced plasticity (TWIP) steel with relatively no microtexture. In this study, electron backscattered diffraction technology was used to quantitatively characterize the heterogeneous plastic strain after a slow strain rate test with hydrogen charging, and the deformation mode and HIC initiation mechanism were clarified. From a statistical analysis of more than 100 grain boundaries, the cracked grain boundary and its vicinity have high heterogeneous strain; that is, the geometrically necessary dislocation density is high, and vice versa. Therefore, high strain incompatibility is the key factor for HIC initiation.

Combined Tension-Shear Failure of Ductile Materials

Failure of ductile materials is usually expressed in terms of effective plastic strain. Ductile materials can fail by two different failure modes, shear failure and tensile failure. Under dynamic loading, shear failure has to do with shear localization and formation of adiabatic shear bands. In these bands plastic strain rate is very high, dissipative heating is extensive, and shear strength is lost. Shear localization starts at a certain value of effective plastic strain, when thermal softening overcomes strain hardening. Shear failure is therefore represented in terms of effective plastic strain. On the other hand, tensile failure comes about by void growth under tension. For voids in a tension field there is a threshold state of the remote field for which voids grow spontaneously (cavitation) and the material there fails. Cavitation depends on the remote field stress components and on the flow stress. In this way failure in tension is related to shear strength and to failure in shear. Here, we first evaluate the cavitation threshold for different remote field situations, using 2D numerical simulations with a hydrocode. We then use the results to compute examples of rate dependent tension-shear failure of a ductile material.

Investigation of mechanical properties of laser welded dual-phase steels at macro and micro levels

The current automotive industry uses new technology in materials processing and lightweight materials to minimize vehicle weight and fuel consumption. As a result, Tailor-Welded Blanks (TWB) are used in regions where additional strength or stiffness is necessary in body-in-white, thus decreasing weight. In this paper, TWB were produced by joining DP600 with 1.8 mm and DP800 with 0.8 mm and 1.5 mm using CO2 laser welding. The effects of laser power and welding speed on the mechanical properties of TWB were investigated. The flow behaviors of the TWB were obtained from tensile tests. The microstructures of the weld zones of the base materials and TWB were revealed, and the numerical analyzes of the microstructures were performed by micromechanical modeling with a 2D representative volume element (RVE). Effective stress and plastic strain distributions in the microstructures and macroscopic flow curves of the base materials and the weld zones were obtained. The uniaxial tensile tests of the samples were modeled, and the flow behaviors of the TWB were obtained with micromechanical modeling. The results showed a significant change in stress distribution and strain localization depending on the grain size of constituents and the thickness ratios of the TWB at micro and macro scales, respectively. The numerical flow curves obtained using the RVE method were in good agreement with those of the experimental.

A new path-independent variable to model ductile damage

ABSTRACT The effective plastic strain is a commonly used damage variable within continuum damage framework. The value of effective plastic strain at fracture, however, depends on strain rate, temperature and strain path. An alternate state variable is proposed in this work that can provide a unique path-independent 2 fracture locus. The average dislocation density is a microstructure-based state variable and has been established in the past to describe the constitutive behaviour of plastic deformation. It is demonstrated that when the average dislocation density is used to model fracture initiation, the fracture locus is unique over a range of strain rates, unlike the conventionally used fracture strain.

Simulation of crystal plasticity in irradiated metals: A case study on Zircaloy-4

A classical crystal plasticity formulation based on dislocation slip was extended to include the mechanisms of dislocation channelling, with associated strain softening which is observed in many alloys post irradiation. The performance of the model was evaluated against experimental data on Zircaloy-4, which included engineering stress-strain response and high-resolution digital image correlation strain mapping. Variants of the model were developed to evaluate the influence on the strain hardening law used, comparing hardening based on a linear relationship for effective plastic strain with that based on the evolution of geometrically necessary dislocations. In addition, governing equations for simulating the interaction between gliding dislocations with various types of irradiation defect were investigated; this included the comparison of isotropic and anisotropic interactions based on the resultant reaction segments for each interaction. It was shown that the engineering stress-strain response measured by experiment could be captured by many of the model variants, but the simulation of characteristic strain heterogeneity was more sensitive to the model used. Direct modelling of the HRDIC experiments indicated that the model successfully predicted the activation of slip systems in many cases and exhibited localised strain distribution as observed in the experiment. In all models localised kink band formation was predicted, which is not observed experimentally, which highlights limitations in modelling of softening materials with a local crystal plasticity approach and a required area of development going forward.

Effect of Strain Rate and Friction on Formability According to Major Deformation Modes in Sheet Metal Forming

The effects of strain rate and friction on the formability of the steel sheet are studied according to the three major deformation modes that are widely used in the industry. Experiments for circular cup stretch, plane strain stretch, and circular cup drawing are carried out at two speeds of 3 SPM and 30 SPM for SGACUD 0.7 t and DP 590 1.0 t steel sheets. The corresponding finite element simulations are carried out. A constitutive equation, which is a function of strain and strain rate, is used to account for the effect of strain rate on flow stress in the finite element analysis. The formability is evaluated using the polar effective plastic strain (PEPS) forming limit diagram. An experimental equation that takes the sliding velocity into account is utilized in this study. In conclusion, the effects of strain rate and friction are clearly understood; finite element analysis by using the constitutive equation to consider strain rate, and also the friction coefficient model according to the sliding velocity, can be effectively used to predict the formability as forming speed changes for the three deformation modes.

Microstructure and mechanical behavior of Ti/Cu/Ti laminated composites produced by corrugated and flat rolling

Ti/Cu/Ti laminated composites were fabricated by corrugated rolling (CR) and flat rolling (FR) method. Microstructure and mechanical properties of CR and FR laminated composites were investigated by scanning electron microscopy, numerical simulation methods, peel and tensile examinations. The effect of CR and FR was comparatively analyzed. The results showed that the CR and FR laminated composites exhibited different effective plastic strain distributions of the Ti layer and Cu layer at the interface. The recrystallization texture, prismatic texture and pyramidal texture were developed in the Ti layer by CR, while the R-Goss texture and shear texture were developed in the Cu layer by CR. The typical deformation texture components were developed in the Ti layer and Cu layer of FR laminated composites. The CR laminated composites had higher bond strength, tensile strength and ductility.

A thermal activation based constitutive model for the dynamic deformation of AA5083 processed by large-scale equal-channel angular pressing

Aluminum alloy 5083 (AA5083) processed by large-scale Equal-channel angular pressing (ECAP) is an excellent engineering material with great prospects for industrial applications. An accurate assessment of the underlying constitutive relationships with easily determined material constants is critical for the predictive design and informed processing of such structural materials. To develop such a design framework, uniaxial dynamic compressive tests over a wide range of temperatures (293–573 K) were carried out for an ECAP-processed AA5083 alloy. Additionally, the microstructure before and after dynamic loading was characterized by SEM and TEM. Based on the experimental results, a new dynamic constitutive model, based on thermal activation theory, was established to describe the plastic flow behavior of the AA5083 alloy that incorporates the effects of plastic strain, temperature, and strain rate. The input parameters of the new model were determined using a particle swarm optimization (PSO) method. The model predictions show excellent agreement with experimental results, which suggests that the current predictive constitutive model is highly effective in reproducing the dynamic deformation behavior of the large-scale ECAP-processed AA5083.

An Investigation of the Impact of Forming Process Parameters in Single Point Incremental Forming Using Experimental and Numerical Verification

Incremental sheet forming (ISF) is an innovative cold forming operation and has enticed great interests owing to its flexibility and capability to manufacture various complex 3D shapes with low costs and minimum requirements. Single point incremental forming (SPIF) is the most popular type of ISF process and has high quality and less occurrence of defects for the formed products if the operating parameters are achieved and evaluated with high precision. In this study, the impact of tool diameter and forming angle on the forming force, thickness distribution, thinning ratio, effective plastic strain, forming depth and fracture behaviour was explored. AA1050 aluminium alloy and DC04 carbon steel were employed to produce a truncated cone in accordance with the SPIF process. A 3D finite element model was required to achieve a well-established investigation. The SPIF of a truncated cone numerical model was adopted to build a model with the same conditions as of the experimental work with aid of ANSYS software version 18 through using the workbench LS-DYNA model. The sheet metal modelling was carried out in accordance the Cowper Symonds power law hardening by taking the behaviour of the material as elastic–plastic, and the anisotropic properties were assumed to simulate the plasticity behaviour for two sheet metals. Results indicate that the DC04 carbon steel has a higher forming force, minimum thickness and lower thinning ratio compared with AA1050 aluminium alloy under the same operating conditions.

Elucidating the influence of temperature and strain rate on the mechanics of AFS-D through a combined experimental and computational approach

In this study, the temperature and strain rate dependent physics of Additive Friction Stir Deposition (AFS-D) are elucidated for the first time. Candidate constitutive models are selected to account for the severe plastic deformation and wide ranges of temperature and strain rate inherent to AFS-D. Torsion mechanical tests are performed to capture AA6061 stress dependency on temperature and strain rate. Four constitutive models, including a low fidelity-calibrated one, are applied to single-layer AFS-D simulations. The robust meshfree method, smoothed particle hydrodynamics (SPH), provided the framework for constitutive model comparison. Utilizing the SPH simulations, peak values, temperature contours, effective stress contours, effective plastic strain contours, build profiles, and simulation run time are all compared to reveal hidden mechanisms of AFS-D processing. This work highlights the importance of constitutive model selection, which can lead to improved simulation results by accurately capturing plastic stress dependence on strain, strain rate, and temperature.

A Multiphysics Model for Predicting Microstructure Changes and Microhardness of Machined AerMet100 Steel.

The machined-surface integrity plays a critical role in corrosion resistance and fatigue properties of ultra-high-strength steels. This work develops a multiphysics model for predicting the microstructure changes and microhardness of machined AerMet100 steel. The variations of stress, strain and temperature of the machined workpiece are evaluated by constructing a finite-element model of the orthogonal cutting process. Based on the multiphysics fields, the analytical models of phase transformation and dislocation density evolution are built up. The white layer is modeled according to the phase-transformation mechanism and the effects of stress and plastic strain on real phase-transformation temperature are taken into consideration. The microhardness changes are predicted by a model that accounts for both dislocation density and phase-transformation evolution processes. Experimental tests are carried out for model validation. The predicted results of cutting force, white-layer thickness and microhardness are in good agreement with the measured data. Additionally, from the proposed model, the correlation between the machined-surface characteristics and processing parameters is established.

Study of grain boundary orientation gradients through combined experiments and strain gradient crystal plasticity modeling

A combined experimental and strain gradient crystal plasticity framework is presented for studying the development of orientation and misorientation gradients at the grain boundaries during plastic deformation. The regions in the vicinity of prior-deformation grain boundaries experience localized plastic deformation and are referred to as Near Boundary Gradient Zones (NBGZs). Deformed microstructures of an aluminum–magnesium (Al–6wt.% Mg) alloy are studied using Electron Back Scattered Diffraction (EBSD) during progressive tensile deformation. Orientation and misorientation gradients at the prior-deformation grain boundaries are quantified on grain pairs with different combinations of crystallographic orientations. Realistic virtual microstructures are then simulated using a strain gradient crystal plasticity finite element framework to study the evolution of local misorientations, stresses and strains and their correlation with the underlying substructure. The simulated microstructures indicate that the average profiles of the Geometrically Necessary Dislocation (GND) density correlates with the local misorientation, while the average profiles of the Statistically Stored Dislocation (SSD) density correlates with the effective plastic strain in these NBGZs. The combined experimental and modeling analysis reveals that the width (mean with deviation) of the distribution of the length of NBGZs, normalized by the grain size, scales with the initial grain-average Schmid factor. Further, our results also suggest a possibly strong correlation between the length of the NBGZ and the grain size.

Fractal characteristic of corroded steel surface and application to the fracture analyses

To analyze the effects of morphological characteristics on fracture behaviors of corroded steel, the morphology analysis, tensile test and corresponding finite element (FE) simulation were systematically performed to investigate the morphological evolution and the degradation of mechanical property of corroded steel. The results indicated that the size parameters (C and W) followed the Chi-square distribution, and the fractal character was obviously observed on corroded steel, especially for critical corrosion pit. The fractal dimension of critical corrosion pit (D*) was a key factor influencing the mechanical property and fracture behavior for corroded steel due to the advantage in systematacially reflecting the morphological characteristics, the agreement with the various mechanical parameters was obvious more than C or W of critical corrosion pit. Comparing the toughness parameters (α and η) among different corroded specimens, the effect of the oxide passivation layer on fracture toughness properties of corroded steel was revealed, and modified. Finally, the characterization of D* on fracture toughness parameters (α, η, effective plastic strain εpcritical and stress triaxiality T) of corroded steel was discussed

Punch-less and die-less sheet hydroforming process for manufacturing of serpentine-shaped micro-channels in ultra-thin sheets

In the present work, novel serpentine-shaped micro-channels were successfully fabricated in ultra-thin sheets of AA1050, C101, and SS304 materials using the sheet hydroforming (SHF) process. In-house fabrication methods, namely punch-less SHF and die-less SHF processes were designed and developed on a 20-t press to manufacture these channels. The finite element (FE) modeling of both processes was developed for the prediction of the deformation behavior of these sheets. The elasto-plastic FE models incorporated the elastic properties, Barlat 89 anisotropic yield model, and Hollomon hardening law for all the three sheets, and their corresponding forming limit diagrams (FLDs) were implemented as damage criteria. It was observed that the maximum pressure was 28 MPa and 32 MPa for the punch-less and die-less SHF process, respectively. The manufacturability of the hydroformed channels was examined through channel depth, aspect ratio, and thickness distribution. The average channel depth and aspect ratio were found to be higher in the case of the die-less SHF compared to punch-less SHF. The failure occurred in the AA1050 channel under plane strain deformation mode near the die corner region and punch corner region for punch-less and die-less SHF processes, respectively, indicated by a sudden dip in the thickness distribution profile. Moreover, the surface quality of the formed channels was investigated through surface roughness value, and this was further correlated with effective plastic strain incurred in the deformation process. It was observed that the surface roughness of the deformed channels fabricated by the punch-less SHF process was lower than those formed through the die-less SHF process in the present study.

Damage Assessment of Simply Supported Double-Pier Bent Bridge under Heavy Truck Collision

Studying the failure or collapse mechanism of an entire bridge under vehicle–pier collision has engineering demand and practical meaning, while the existing damage assessment work mainly focuses on the impacted pier. This study aims to numerically clarify the collapse mechanism and evaluate the damage level of the entire bridge. First, the previously validated finite-element (FE) model of a simply supported RC bridge with double-pier bent when impacted head-on by a heavy truck. The model improved by incorporating the nonlinear behaviors and damage of the bridge superstructure. According to the truck mass and impact velocity involved in the actual collision accidents, 20 truck–pier collision scenarios are designed and numerically simulated by adopting the nonlinear FE program LS-DYNA. The damage/failure or collapse mechanism of the entire bridge, as well as the vehicular impact force and bridge structural dynamic behaviors, are examined. It shows that (i) the overall collapse of the bridge structure is an impact-successive and damage-accumulative process, which is not completely coincident with the failure of impacted pier; and (ii) the cargo-induced internal forces of the impacted pier have two peaks attributed to the initial contact and the following pushing–drag effect of cargo, respectively. Then, based on the damaged area of concrete and effective plastic strain of reinforcement, the damage levels of the main bridge components, including the pier, bent cap, tie beam, pile, girder, and deck, are qualitatively assessed and classified, followed by the clarifications of their corresponding inner correlations. Furthermore, by proposing two quantitative damage indexes, a feasible on-site approach for assessing the post-collision damage of the bridge structure is established and validated by eight additional collision scenarios, and the dependency of bridge damage level on both the vehicular impact velocity and mass is graphically presented. The proposed approach can be practically generalized to on-site damage evaluation of a bridge structure after actual accidents and can provide useful reference in design and restoration of RC bridges.

Effect of Hydroforming Drawing Cups on Thickness Variation and Surface Roughness

Recently, hydroforming was developed to address the emerging problems encountered by the conventional rigid tool-based deep drawing process. Hydroforming is a specialized type of die forming process, that uses a rigid die while the pressure provided by the liquid acts as a punch to shape the sheet metal. The current paper is directed to study the hydroforming process numerically and experimentally as a means for shaping aluminum alloy sheets based on the quality of product thickness variation and surface roughness. Moreover, it offered a comparative investigation of the experimental and numerical findings of this process. Therefore, thickness variation has been calculated numerically by designing a numerical model using Marc software which fits in large deformation simulation. On the other hand, thickness variation and surface roughness were measured experimentally along drawn cups and compared with the numerical results. The numerical results of thickness variation are matched with the experimental results. Furthermore, surface roughness was measured and compared before and after drawing at five regions. Since there is no contact between the upper side of a cup and any metallic parts, surface roughness depends only on the effect of plastic strain and was found to be increased in all regions.

Investigation on deformation of DP600 steel sheets in electric-pulse triggered energetic materials forming

Electric-pulse triggered energetic materials forming (ETEF) is a high-speed manufacturing process, which utilizes the chemical energy released by energetic materials (EMs) triggered by underwater wire discharge to plastically shape metals. ETEF is not fully understood, particularly in research on the discharge characteristics of energetic materials triggered by metal wires and the deformation process of metal sheets. The above two problems were investigated in this paper using experimentation and numerical simulation. For the pulse discharge characteristics, the peak values of voltage and current were reduced during the triggering process of energetic materials, and the triggering energy consumption of energetic materials was quantified to be about 200 J. The matching parameters of different capacitor-voltage devices may be insensitive to triggering the energy release of energetic materials. The maximum major strain and thinning rate of the bulged specimen under ETEF conditions were significantly reduced when compared to the quasi-static specimen with the same bulging height, and the specimen’s deformation uniformity and strain distribution were improved. The simulation results showed that the addition of energetic materials significantly improved the plastic strain energy of the blank. The deformation of the blank in ETEF can be divided into two stages: the initial chemical energy action stage and the inertia action stage. The bulging height of sheet metal increased by nearly 301% in inertia action stage, accounting for 80% of the total deformation time, and the effective plastic strain distribution was more uniform.

Strain localization and crack initiation behavior of a PM Ni‐based superalloy: SEM‐DIC characterization and crystal plasticity simulation

AbstractThe strain localization and crack initiation behavior of a powder metallurgy (PM) nickel‐based superalloy FGH4098 under low cycle fatigue (LCF) loads at room temperature is investigated by combining scanning electron microscope (SEM)‐digital image correlation (DIC) characterization with crystal plasticity simulation. The elastic anisotropy near annealing twin boundaries contributes to strain localization and results in high propensity of LCF failure. The effect of local microstructure on the fatigue crack initiation at {111} slip bands and tortuous crack propagation is revealed. Meanwhile, local crystal plasticity finite element cyclic deformation simulation is carried out based on explicit microstructure reconstructed from electron backscatter diffraction (EBSD) characterization. Four metrics of accumulated shear strain, effective plastic strain, shear strain energy dissipation density, and Fatemi–Socie parameter are selected as fatigue indicator parameters to predict crack initiation site. Fatemi–Socie parameter is proved to be a promising metric for crack initiation prediction.

An Investigation for the Performance of the Design of Hot Forging Die and Workpiece

Hot forging is a metalworking process in which metals are plastically deformed above their recrystallization temperature, allowing the material to retain its deformed shape as it cools. In today's industry, the performance of the tools used during the hot forging process has always been a subject of interest. Although it is known that, the tool life used affects 10% of the design costs of the total budget, 80% of the total production costs are determined during the design stages. For this reason, minimizing mechanical stress and changing the die design, so as to optimize the tool life and reduce the cost, have been attractive. In this study, finite volume analysis was performed on 31CrV3 steel using the multi-stage forming process of hot closed die forging using Simufact Forming v16 software. 56NiCrMoV7 hot work tool steel was used as die material and X153CrMoV12 as template blade raw material. In this article, 3 state variables, effective plastic strain, equivalent stress and temperature were evaluated for two different die designs of multi-stage forming processes such as pre-forming, final forging, and cutting. The results were compared for cost for single and dual dies. For both die designs, the initial temperature of the billet is 1100-1200 ºC and the die temperature is 100-110 ºC. Finally, comparative analyzes of both die designs for three state variable parameters were performed in terms of mechanical properties and cost. The main focus is on calculating mechanical properties and cost based on available process parameters using subroutines during the incorporation of different die designs. According to the results obtained from the simulation study, the manufacturability of the product has been proven, the effect of the changes in the die and workpiece design on the cost have been investigated, and the final performance has been revealed by evaluating the profit rate.

Quantitative characterisation and modelling of the effect of cut edge damage on the magnetic properties in NGO electrical steel

The cut edges of electrical steel NGO laminations in electric motors experience mechanically induced plastic deformation and residual elastic stress, which deteriorate the magnetic performance of the material. This deterioration is accounted for empirically in electric machine modelling tools by introducing a ‘build factor’ on the iron losses. Currently, a wide range of cut edge deteriorated widths have been reported in the literature, depending on the method used for characterisation, the material and the cutting method. In this paper, cut edge plastic damage characterisation was carried out using EBSD kernel average misorientation (KAM) maps and nano-indentation to quantify the magnitude and width of the plastic damage at the cut edge for a stamped tooth of a segmented stator and a guillotined single sheet tester (SST) sample. The relationship between the EBSD KAM and nano-hardness values and plastic strain was found using tensile samples tested to varying applied strain levels. Therefore, the plastic strain gradient with respect to distance from the cut edge was determined. It was found that both EBSD and nano-indentation gave similar predictions of effective plastic strain values and damage width: up to 1.45–1.50 at stamped cut edge over 180 µm width and up to 1.35–1.4 at guillotine cut edge over 250 µm width. The relationships between the magnetic performance and elastic stress, plastic strain, and plastic strain with elastic stress were determined using single sheet tester (SST) measurements. In addition, SST 3D FEA models of the cut edge sample were built using COMSOL Multi-Physics software considering a single layer for plastic damage only and two layers for plastic damage + elastic stress and elastic stress. The modelling results for the guillotine cut edge SST samples were compared to measured data. It was found that to obtain accurate cut edge magnetic property deterioration for NGO electrical steel laminations both the plastic strain and residual elastic stress cut edge effects need to be included. In the cut edge model, a first layer width of 250 µm with magnetic properties for an effective plastic strain of 1.17 under residual compressive elastic stress of −133 MPa and a second layer width of 220 µm with magnetic properties for residual compressive elastic stress of −119 MPa give excellent results for hysteretic BH curves and specific iron loss evaluation.