Effective Plastic Strain Distribution Research Articles

Shakedown of metallic sandwich beams when subjected to repeated impact loadings

When a monolithic metallic beam/plate subjected to repeated dynamic loadings with fixed impact level experiences elastoplastic deformation, its measurable deformations may cease to develop for further repetitions of the same dynamic load: this phenomenon was referred to as “pseudo-shakedown” in previous studies (Jones, 2014; Shen and Jones, 1992). Would pseudo-shakedown occur in a metallic sandwich structure under repeated shock loadings remains elusive. A combined experimental and numerical study was carried out to explore whether dynamic shakedown could occur in all-metallic ultralightweight corrugated core sandwich beams. For repeated impact tests, the sandwich beams were fabricated via the sequential process of cutting-stamping-vacuum brazing. When subjected to repeated impact loads (achieved via aluminum foam projectiles launched from a light gas gun), the dynamic responses of each sandwich specimen - including structural evolutions, beam deflections, and deformation/failure modes - were measured. Experimental results revealed that, depending upon the level of impact momentum applied to the sandwich beam, either dynamic shakedown or progressive failure could occur. The method of finite elements (FE) was subsequently employed to simulate the repeated shock tests, which was validated against experimental measurements, with good agreement achieved. To explore the physical mechanisms underlying the observed dynamic shakedown, the FE results of final plastic energy and effective plastic strain distribution in the sandwich beam were extracted and analyzed. When shakedown occurred, the measurable permanent deformation of the sandwich beam kept a relatively stable state, but its plastic energy remained positive, which is different from its monolithic beam/plate counterpart (i.e., plastic energy dropping to zero during dynamic shakedown). Such difference is mainly attributed to stress concentration occurring at the connecting joint points between the corrugated core and face sheets of sandwich and clamped endings, which produces plastic deformations that are difficult to reflect in overall large deformations of the beam. Consequently, the dynamic shakedown of metallic corrugated core sandwich beam captured in this study appears to be inexhaustive and hence may be termed as the “apparent pseudo-shakedown” (with danger lurking in the welding joints as well as clamped endings). Finally, based on a simplified bi-linear hardening constitutive law, the mechanisms underlying the dynamic shakedown of sandwich beam were further discussed from a purely base material point of view.

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.

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.

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.

An Improvement in Constrained Studded Pressing for Producing Ultra-Fine-Grained Copper Sheet

In this study, constrained studded pressing (CSP) was modified to produce ultra-fine-grained copper sheets and is called modified-CSP. In modified-CSP, due to the selection of asymmetric semicircle studs, the maximum groove depth can increase up to three times the sheet thickness. In the CSP method, the groove depth is selected to be equal to the sheet thickness. To investigate the effective plastic strain, a finite element model (FEM) of modified-CSP was established. For this purpose, DEFORM-3D commercial software was used. A simulation showed that the modified-CSP process was capable of using higher strain, about 0.8 in each pass than in CSP. Copper sheets were deformed up to 10 passes by modified-CSP. The microstructure of the produced samples was analyzed. The results show that the grain size decreases in the first pass. In addition, with increasing plastic strain, the structure of the twins bands was observed. Mechanical properties, including tensile properties and Vickers microhardness, of the samples during the process were investigated. The strain inhomogeneity factor (SIF) and the hardness inhomogeneity factor (HIF) were used to quantitatively express the uniformity of distribution of effective plastic strain and Vickers microhardness, respectively. Compared with CSP and constrained groove pressing (CGP), the results showed that although the ultimate tensile strength (UTS) has significantly increased, the ductility values have remained almost constant. Moreover, in modified-CSP, the load-die stroke diagram increases almost evenly due to the removal of the stud interface area and progressive engagement. Therefore, modified-CSP copper sheets showed superior tensile properties such as good toughness.

Numerical Investigation of Plastic Strain Homogeneity during Equal-Channel Angular Pressing of a Cu-Zr Alloy

A three-dimensional finite element method (3D FEM) simulation was carried out using ABAQUS/Explicit software to simulate multi-pass processing by equal-channel angular pressing (ECAP) of a circular cross-sectional workpiece of a Cu-Zr alloy. The effective plastic strain distribution, the strain homogeneity and the occurrence of a steady-state zone in the workpiece were investigated during ECAP processing for up to eight passes. The simulation results show that a strain inhomogeneity was developed in ECAP after one pass due to the formation of a corner gap in the outer corner of the die. The calculations show that the average effective plastic strain and the degree of homogeneity both increase with the number of ECAP passes. Based on the coefficient of variance, a steady-state zone was identified in the middle section of the ECAP workpiece, and this was numerically evaluated as extending over a length of approximately 40 mm along the longitudinal axis for the Cu-Zr alloy.

Effect of hardening law and process parameters on finite element simulation of single point incremental forming (SPIF) of 7075 aluminum alloy sheet

In the last two decades, the advances of using computers in sheet metal forming processes have introduced a novel adjustable process known as incremental sheet forming (ISF) as an optimal method for fast prototyping and low numbers of production. Formability and deformation behavior of ISF process are highly affected by the selected process parameters, such as the toolpath, step size, tool diameter, feed rate, and lubrication. The purpose of this work was to study the effect of these process parameters as well as hardening law on single point incremental forming (SPIF) process. For this work, a truncated-cone geometry was considered as a target shape with 7075-O aluminum alloy sheets. The simulations were conducted with different process parameters, i.e., toolpath type, step size, tool size, feed rate, friction coefficient, and wall angle with respect to the tool force and moment, effective plastic strain distribution and thickness of the part. In addition, three types of hardening laws i.e., isotropic extended Voce type hardening law, combined isotropic-kinematic Chaboche type hardening laws with single and double back-stress terms were applied in the finite element simulation of SPIF process. A detailed comparison of these hardening laws' predictions was made with respect to the tool force and moment, effective plastic strain distribution and thickness of the part.

Investigation of accurate forming of a semi-ellipsoidal shell part by an electromagnetic forming method

Forming a sheet into a predesigned die cavity is an effective way to improve the dimensional accuracy of deformed parts. However, it is difficult to obtain good die-fitting quality for workpiece deformed at high speed during the one-time discharge electromagnetic forming (EMF) process. To address this challenge, a numerical simulation model was established to help optimize the forming process that affects the die-fitting quality in the formation of a semi-ellipsoid shell part. Then, experiments were conducted according to the optimized forming process. Finally, the dynamic deformation behavior of the workpiece was revealed. The results showed that the drawing deformation mode can effectively improve the die-fitting quality as well as the effective plastic strain distribution of the shell part compared with the bulging deformation mode. Moreover, reducing the initial blank diameter is a more effective way to improve draw-in compared with adjusting the blank holder force. Furthermore, a semi-ellipsoid shell part was manufactured with a maximum die-fitting gap of no more than 1.4 mm at a one-time discharge voltage of 11.5 kV. The deviation was only 1.45% of the maximum forming height. The results provide a foundation for forming a large semi-ellipsoidal shell part by the one-time discharge EMF method.

Stability analysis of the Xinlu Village landslide (Chongqing, China) and the influence of rainfall

On June 28, 2016, a landslide occurred in Xinlu Village, Qijiang District, Chongqing, China. The landslide volume was 854,200 m3. Exposed to continuous rainfall, the rocky part of the trailing edge slipped first, and then the soil part of the leading edge was pushed downward. Numerical simulations were used to analyze the formation characteristics of the landslide and to predict the stability of the landslide after the slip. In order to ensure the accuracy and rationality of numerical calculation, we used field surveys, laboratory tests, and back-calculation to restore the typical sections, determine the relevant mechanical parameters, and control boundary conditions. The displacement, stress, effective plastic strain distribution, and safety factor, obtained by numerical calculation, were compared to examine the action of rainfall. According to the evaluation of landslide stability and numerical calculation results, the Xinlu Village landslide remained in a peristaltic stage after the initial overall sliding, and additional sliding could occur under storm conditions.

Finite Element Analysis of Single Point Incremental Forming (SPIF) of Aluminum 7075 Using Different Types of Toolpath

To make large number of parts in automotive, aerospace, and appliances industries, sheet conventional metal forming processes, such as stamping, are used. However, for small number of productions, novel flexible manufacturing processes, such as incremental sheet forming (ISF) must be utilized to decrease the production costs. Studying the process parameters in ISF process such as, the toolpath, step size, tool size, feed rate, lubrication, and wall angle is essential as they are affecting the formability and deformation behavior of this process. The purpose of this study was to investigate the effect different types of toolpath, such as z-level (profile) and helical (spiral) to form a truncated-conical geometry in simulation of the single point incremental forming (SPIF) of AA7075-O. A detailed comparison of these tool paths' predictions was made with respect to the effective plastic strain distribution, part thickness, tool force and moment.

Parametric Analysis for Minimizing the Edge Waves in the Roll Forming

To identify the cause of edge waves and to minimize them, which are frequently occurring on the steel pipe manufacturing site, the shape of the edge part of skelp has been confirmed according to a design variable and operating condition. In particular, parametric studies were carried out on the variation in the thickness of skelp, tskelp, the roll gap between upper and bottom rolls, troll, at the forming stage 1, Forming 1, the roll shape, toffset, of the Forming 1, and the material property of skelp to study the generation of edge waves, because these parameters have been determined by field engineers extemporaneously without any physical estimation. For this purpose, the roll design and operating conditions used in the field were applied to the finite element analysis model, and the distribution of contact force between the rolls and skelp, and the distribution of effective plastic strain on the skelp were investigated. The fact that adjusting to tskelp and troll arbitrarily without changing to the roll shape can cause not only the edge waves but also the center waves, was carried out. Especially, the edge waves were reduced without the irregular contact pressure by changing the surface of the upper roll that is offset by target tskelp in the normal direction of the surface of the bottom roll in the Forming 1, when the target thickness is tskelp. Moreover, there is no significant difference in the vertical load applied to the rolls when high-strength steels are used or when low-strength steels are used, it is necessary to predict the local maximum and minimum of contact pressure between the skelp and rolls and the shape of the upper roll of the Forming 1 should be modified to decrease irregular contact pressure instead of any design modifications.

A Numerical Study on the Thermo-mechanical Response of a Composite Beam Exposed to Fire

This study presents an analytical framework for estimating the thermo-mechanical behavior of a composite beam exposed to fire. The framework involves: a fire simulation from which the evolution of temperature on the structure surface is obtained; data transfer by an interface model, whereby the surface temperature is assigned to the finite element model of the structure for thermo-mechanical analysis; and nonlinear thermo-mechanical analysis for predicting the structural response under high temperatures. We use a plastic-damage model for calculating the response of concrete slabs, and propose a method to determine the stiffness degradation parameter of the plastic-damage model by a nonlinear regression of concrete cylinder test data. To validate simulation results, structural fire experiments have been performed on a real-scale steel–concrete composite beam using the fire load prescribed by ASTM E119 standard fire curve. The calculated evolution of deflection at the center of the beam shows good agreement with experimental results. The local test results as well as the effective plastic strain distribution and section rotation of the composite beam at elevated temperatures are also investigated.

Transient behaviour of grouted connections of offshore wind turbines subject to ship impact

Grouted connections are a critical structural element of monopile-supported offshore wind turbines (OWTs), connecting turbine towers with foundation piles. Due to engineering requirements, they are normally installed at the mean water level (MWL), leading to high risk of ship collisions. In this study, transient response and damage analysis were performed on the grouted connections of monopile OWT when subjected to ship impacts. Taking into account the sandwich construction of the grouted connection of the OWT and the non-linear behaviour of the structure materials, a finite element model of a vessel of 2000-ton displacement collision with a 5 MW monopile OWT was developed using explicit finite element code LS-DYNA. The ship was assumed to strike head-on and at the middle of the grouted connection. Characteristics of the collision system in terms of energy, velocity, impact force and the response of the ship and the grouted connection were analysed. Internal contact forces, stress and effective plastic strain distribution of the grouted connection were discussed. Four phases of the collision process were identified: initial collision, motion towards maximum OWT deflection, towards vessel-OWT separation, and after separation. The ship collision response and damage of the grouted connection were considerably influenced by the strain rate effect of the structure materials. Collided by a ship, even at a low velocity of 2 m/s, the grouted connection for monopile OWT could suffer heavy or major damage. The current analysis sheds light on the dynamic response of grouted connections of monopile OWTs to ship impact. It lays a solid foundation for future analysis on the design of grouted connections of OWTs.

3D FEM simulations and experimental validation of plastic deformation of pure aluminum deformed by ECAP and combination of ECAP and direct extrusion

Rigid-viscoplastic 3D finite element simulations (3D FEM) of the equal channel angular pressing (ECAP), the combination of ECAP + extrusion with different extrusion ratios, and direct extrusion of pure aluminum were performed and analyzed. The 3D FEM simulations were carried out to investigate the load–displacement behavior, the plastic deformation characteristics and the effective plastic strain homogeneity of Al-1080 deformed by different forming processes. The simulation results were validated by microstructure observations, microhardness distribution maps and the correlation between the effective plastic strain and the microhardness values. The 3D FEM simulations were performed successfully with a good agreement with the experimental results. The load–displacement curves and the peak load values of the 3D FEM simulations and the experimental results were close from each other. The microhardness distribution maps were in a good conformity with the effective plastic strain contours and verifying the 3D FEM simulations results. The ECAP workpiece has a higher degree of deformation homogeneity than the other deformation processes. The microhardness values were calculated based on the average effective plastic strain. The predicted microhardness values fitted the experimental results well. The microstructure observations in the longitudinal and transverse directions support the 3D FEM effective plastic strain and microhardness distributions result in different forming processes.

Thermal fatigue life evaluation of SnAgCu solder joints in a multi-chip power module

For power devices, the reliability of thermal fatigue induced by thermal cycling has been prioritized as an important concern. The main target of this work is to apply a numerical procedure to assess the fatigue life for lead-free solder joints, that represent, in general, the weakest part of the electronic modules. Starting from a real multi-chip power module, FE-based models were built-up by considering different conditions in model implementation in order to simulate, from one hand, the worst working condition for the module and, from another one, the module standing into a climatic test room performing thermal cycles. Simulations were carried-out both in steady and transient conditions in order to estimate the module thermal maps, the stress-strain distributions, the effective plastic strain distributions and finally to assess the number of cycles to failure of the constitutive solder layers.

Stability analysis of interfacial Richtmyer-Meshkov flow of explosion-driven copper interface

In this paper, a stability analysis is given to study the unstable mechanism of the Richtmyer-Meshkov flow of explosion-driven copper interface. The Richtmyer-Meshkov flow refers as an interfacial instability growth under shockwave incident loading. Numerical investigations are performed to check the applicability of the two-dimensional hydrocode, which is named AFE2D, and the physical models of detonation waves propagating in the high explosives, equations of state and the constitutive behaviors of solids in the analysis of Richtmyer-Meshkov flow problems. Here we theoretically analyze the two key issues of the unstable mechanism in Richtmyer-Meshkov flow in solids. The unstable mechanism includes temperature related melting mechanism and the plastic evolution related tensile fracture mechanism. In the analysis of the temperature related unstable mechanisms, the calculated temperature increase during the shockwave compression from the shock Hugoniot data in the shockwave physics is not enough to melt the material near the perturbed interface. On the other hand, the temperature increase from the translation of plastic work during perturbation growth which relats to the distribution of the cumulative effective plastic strain is also not enough to supply the thermal energy which is needed to melt the crystal lattice of solid, either. Therefore, the temperature related melting mechanism is not the main factor of the unstable growth of copper interface under explosion driven. In the analysis of the plastic tensile fracture related unstable mechanism, a scaling law between the maximum cumulative effective plastic strain and the scaled maximum amplitude of spikes is proposed to describe the relationship between the plastic deformation of material and the perturbation growth of interface. Combined with a critical plastic strain fracture criterion, the unstable condition of the scaled maximum amplitude of spikes is given. If the spikes grow sufficiently to meet the unstable condition, the interfacial growth will be unstable. Numerical simulations with varying initial configurations of perturbation and yield strength of materials show good agreement with the theoretical stability analysis. Finally, a criterion to judging whether the growth is stable is discussed in the form of competition between the temperature related unstable mechanism and the tensile fracture unstable mechanism.

Spatial correlation between local misorientations and nanoindentation hardness in nickel-base alloy 690

Misorientation increases with plastic strain in metals, and this observation has been used as an empirical assessment of plastic strain in recent years. The method has been validated for a sample area corresponding to a 100µm×100µm square, but on the micrometer scale misorientations no longer seem to correlate with plastic strain. Misorientations are however not dependent on plastic strain but rather on dislocation density, which means it should also be related to hardness. Therefore, we have in this work compared maps of predicted hardness calculated from misorientation determination with maps of actual hardness measured by nanoindentation.It was shown that the predicted and measured hardness maps do indeed correlate spatially in nickel-base Alloy 690, although the measured values have a significantly smaller hardness variation. This is explained by a presumably high and uniform density of statistically stored dislocations, which contribute to hardness but do not affect the misorientation determination from electron backscatter diffraction. Thus local misorientation can be used to qualitatively map the local effective plastic strain distribution, for example to identify regions of increased hardness.

Effect of Hardness and Thickness of Nonoriented Electrical Steel Sheets on Iron Loss Deterioration by Shearing Process

The influence of the shearing process on the iron loss of nonoriented electrical steels with the thickness of 0.20-0.50 mm and the hardness of HV150-220 was investigated. The deterioration ratio of iron loss was clearly smaller in thinner or harder samples. The deterioration of iron loss and the droop height, reflecting the amount of plastic deformation, displayed a good relationship irrespective of the material thickness and the hardness. This is a well-known statement that an elastic stress affects losses of steel sheets. The effective plastic strain distribution through the thickness of the sheet calculated by the elastic-plastic analysis based on the finite-element method (FEM) coincided with the actual measurement result of hardness increase, reflecting the distribution of plastic deformation. From the evaluation of elastic-plastic deformation by the FEM, it was also shown that the material thickness and hardness influence the elastic strain distribution as a plastic strain, and that the droop height reflects both the amount of plastic strain and the amount of elastic strain.

A new approach for modeling of streamlined die operations based on a non-quadratic stream function

Talbert and Avitzure introduced the implementation of a quadratic stream function for derivation of velocity field governing through streamlined die extrusion. In the present study, a non-quadratic stream function is introduced to model various streamlined die processes. In the modified formulation an exponent was designated to the stream function in order to obtain a generalized model. The quadratic stream function approach was restricted to processes with axial flow direction. In contrast, the modified model is capable to study the common forming processes i.e. simple and bimetal extrusion and drawing. The actual velocity field was derived from the generalized field by upper bound technique. The plastic flow was studied through distorted bands and elements that obtained by Eulerian description of motion. Subsequently, the modeling of extrusion and drawing proceed by the calculation of the effective plastic strain distribution. Streamlined die has been designed and proposed based on the fact that it requires less external power than the conventional operations and that deforming material encounters smoother plastic flow. The results revealed the length of die highly influences the deformation mode by affecting the shear component of strain. The capability of the modified stream function to capture various metal forming operations with streamlined die was investigated.

RETRACTED ARTICLE: Finite element simulation of material flow in friction stir process of nylon 6 and nylon 6/MWCNTs composite

AbstractIn the current study, a numerical model based on Lagrangian incremental formulation was developed for friction stir process (FSP) of nylon 6 and nylon 6/multiwalled carbon nanotube (MWCNT) composite to investigate the thermomechanical behavior of them (e.g. temperature, effective plastic strain distribution, material flow, and material velocity). For this purpose, FSP was used to disperse the MWCNTs among the polymer matrix of nylon 6, homogenously. The X-ray diffraction and scanning electron microscopy were used to investigate the properties of fabricated nanocomposite. The obtained results were then used to verify the objectives of numerical model. According to the results, the MWCNTs are separated from each other while passing the tool-pin due to high plastic strain applied on them and greater amount of the material accumulates in the AS of stirred zone after passing the tool-pin. Also, MWCNTs were homogeneously and straightly dispersed throughout the nylon 6. The straight and non-curved disper...