Equivalent Strain Distribution Research Articles

Performance evaluation for the domain decomposition method in nonlinear vibration of the composite hard-coating cylindrical shell.

The applications of the modified domain decomposition method in nonlinear vibration analysis of the composite hard-coating cylindrical shells are still at a relatively superficial level, owing to the fact that its performance under different decomposition parameters has not been thoroughly investigated for achieving sufficient precision. A parametric domain decomposition method is developed to facilitate self-performance evaluation in nonlinear vibration analysis of the shell. Correspondingly, in order to avoid a mass of redundant computation of the segment stiffness and material damping matrices during iterations, a specialized preprocessing scheme is designed by pre-establishing the parametric analytical expressions and matrix databases. The resonant response is sensitive to the circumferential segment number, but weakly affected by the axial segment number. The optimum circumferential segment number in the present study is suggested to be Nθ = 70, which can achieve good calculation accuracy and efficiency. Highly consistency is shown for the distributions of axial equivalent strain under different axial segment numbers. Smaller circumferential segment numbers would result in larger equivalent strain and bad solution accuracy. The sufficient solution accuracy of nonlinear vibration of the composite hard-coating cylindrical shell can't be achieved by increasing the axial segment number with constant segment width, but only by enough circumferential segment number, which is fundamentally determined by its equivalent strain distributions and gradients, and is with close relation to the axial and circumferential wave numbers of the shell.

Process parameters impact on the forming quality of conical rotary parts during power spinning

The conical rotary part with variable wall thickness is a typical aircraft engine sheet metal casing, which requires high forming quality. In this paper, the hot power spinning process of conical rotary part with continuously variable wall thickness of superalloy GH4169 was simulated by DEFORM-3D FE (finite element) software. The equivalent stress, equivalent strain and temperature distribution characteristics were analysed to explore the forming mechanism. The single factor variable method was used to explore the influence of three process parameters, namely, the mandrel speed, the roller feed ratio and the spinning temperature, on the forming quality. The wall thickness deviation and the roundness error of the cone outer surface were taken as the evaluation indexes. Excessive thinning rate will produce large equivalent strain, which may lead to work piece fracture. Therefore, appropriate roller feed ratio should be selected to reduce the generation of defects. The results provide a theoretical basis for improving the service life of aero-engine sheet metal casing.

Microstructure Observation, Accumulated Equivalent Stress, and Creep Strain Simulation of SPD Disconnector Solder Joint Based on Isothermal Aging

Surge protective device (SPD) is a widely used type of overvoltage protection device, and the good resistance characteristics of metal oxide varistor (MOV) inside determine its ability to suppress transient overvoltage. However, the deterioration of MOV after long-term operation will make the temperature rise gradually. The disconnector made from disconnection mechanism and low-temperature solder joint can prevent the burning of MOV caused by increasing temperature, and its solder joint inside is vital to the successful disconnection. However, the cracks and voids will gradually appear inside the low-temperature solder joint during the operation, which seriously affects the reliability of SPD. Microstructures of SPD disconnector solder joint were assessed at 20 °C (natural operation) and 135 °C (aging operation) in this article. Besides, the energy-dispersive spectrometer (EDS) is used to compare the compositions and element migration at 20 °C and 135 °C. Furthermore, the accumulated equivalent stress and creep strain distribution on cracks and voids in solder joint are analyzed by the finite-element analysis (FEA). It is shown that the solder joint at 135 °C not only changes its microstructures and compositions compared 20 °C but also appears larger voids and cracks. Their appearance is due to the large accumulated equivalent stress and creep strain by analyzing the 2-D simulation model of the solder joint. Moreover, the increase of the radius of electrode corners can effectively reduce the accumulated equivalent stress and creep strain, and it will slow down the generation of cracks and voids and improve the reliability of SPD operation.

Predicting rupture locations of ascending aortic aneurysms using CT-based finite element models

Accurate rupture risk assessment of ascending aortic aneurysms is important for reducing aneurysm-related mortality. More recently, computational models have been shown to better predict rupture risk than diameter-based measurements. However, it remains unclear whether finite element (FE) models of the ascending aorta can predict rupture location, and over what timeframe those predictions are reliable. The aim of this study was to evaluate FE models of the ascending aorta generated from computed tomography (CT) scans in predicting rupture location. Pre- and post-rupture CT scans were obtained of 12 patients who underwent emergency surgical repair for ascending aorta rupture with varying time intervals between scans (20 days – 6 years). A rigid iterative closest point (ICP) registration was used to overlay post-rupture aortic geometries with pre-rupture FE models and directly compare predicted regions of high equivalent strain with actual rupture. The FE model predicted the rupture location in the 5 patients with the shortest time intervals between the pre- and post-rupture scans (20 days – 2 years, 3 months). However, rupture location was not predicted in the 4/5 patients with greater than 3 years between scans. Achieving a physiological equivalent strain distribution in the FE model was highly dependent on the resolution of the pre-rupture scan and whether contrast agent was present. The results suggest there may be a time interval beyond which FE predictions of rupture location may not be reliable. The results in this study may help clinical validation of FE models of ascending aortic aneurysms predicting rupture risk.

Elements of Designing Upholstered Furniture Sandwich Frames Using Finite Element Method.

This paper presents an approach to the design of an upholstered furniture frame using the finite element method and empirical studies. Three-dimensional discrete models of upholstered furniture frames were developed taking into account orthotropic properties of solid pine wood (Pinus sylvestris L.) without and with details strengthening their structure in the form of glue joints and upholstery staples. Using the CAE Autodesk Inventor Nastran finite element method, linear static analyses were performed by simulating normative loading. The finite element method was performed considering the experimentally determined stiffness coefficients of the PCAC adhesive and staple joints. As a result, stress, displacement, and equivalent strain distributions were obtained for upholstered furniture frame models with stapled corner joints. The deformation and strength behavior of the upholstered furniture frames was improved by reinforcing with a wood strip. A new approach to the design of upholstered furniture frame frames using the FEM method with stapled component connections was developed and tested. The results of the study can be applied in the optimization of upholstered furniture construction.

Effect of heterogeneous microstructure on the mechanical properties and deformation behavior of rotating backward extruded ZK61 alloy

The rotating backward extrusion (RBE), as a novel severe plastic deformation process, has prosperous industrial application prospect. However, the capability and potential of the RBE process to prepare samples with different heterogeneous microstructures has not attracted attention. In order to explore the relationship between different microstructural compositions and mechanical properties of tubular component prepared by RBE process, the grain size distribution, grain orientation and mechanical properties of a ZK61 Mg alloy tubular component prepared by the RBE process in different regions (along the wall thickness and height directions) were investigated. The results show that the microstructure evolution in different regions is closely related to the equivalent strain distribution. The grain refinement effect is positively correlated with the equivalent strain, but a higher applied strain also leads to a strong basal orientation and high residual stress. Furthermore, the tensile deformation behavior of different samples revealed that samples with preferentially microstructural compositions (volume fraction of fine grains: 40∼60%) have better work hardening capability and strong-toughness synergy. This is mainly attributed to more effective coordinated deformation between different regions (fine grain region and coarse grain region), which can relieve local stress concentration and accommodate more dislocations. In contrast, an excessively high volume fraction of fine grains in samples limits their ability to store dislocations that saturate rapidly with increasing strain, while an excessively low volume fraction of fine grains in samples has difficulty accommodating the high density dislocations transferred from the coarse grain region, resulting in accumulation of high local stress at the interfaces of different regions (fine grain region and coarse grain region). Both of the above can deteriorate the work hardening ability and comprehensive performance, causing the sample to fail before sufficient work hardening occurs.

The Role of Interfacial Adhesion on the Mechanical Behavior of Thin Metal/Polymer Laminate with Surface Roughness.

Metal/polymer laminate has versatile applications in industry due to the essential roles of its constituents in controlling its mechanical behavior. Therefore, efforts to enhance a laminate’s performance should target its mechanical behavior. One of the most influencing features of the mechanical behavior of this type of thin laminate is the interface layer properties. This study concentrates on the mechanical response of thin aluminum (Al) foil deposited on a polymer substrate by calibrating its interfacial layer properties based on available uniaxial tensile tests performed on thin Al/polymer laminate. Then, taking into account the calibrated parameters for the interface layer, which leads to mimicking the real conditions of the laminate, one type of imperfection is introduced as a wavy roughness on the surface of each layer with different amplitudes to investigate its influence on the overall mechanical behavior of the laminate and its failure mode. The results highlighted that the existence of the roughness on the surface of the polymer layer reduces the maximum engineering stress of the laminate more severely compared to other conditions. As the roughness amplitude increases, the maximum stress reduces a lot. The distribution of equivalent plastic strains represents the appearance of the shear bands in the Al layer and an almost uniform distribution for the polymer layer. In the case of existing roughness on each layer, a higher amount of plastic strain accumulation occurs in the middle of the polymer layer and top corners of the thin Al layer. Due to the significant effect of interfacial layer properties to improve the maximum strength of the laminate and its final elongation, a parametric study is performed, taking into account different interfacial properties. The results indicate that laminate behavior with weaker separation properties in the interface layer is mostly unaffected by adopting higher tractions, and no change happens in the case of high separation considering weak tractions.

High-Order Groove-Shape Curve Roll Design for Aluminum Alloy 7075 Wire Rolling

A Bézier curve groove-shape roll design method was proposed and compared to round-oval-round designs for the wire rolling process. CAE simulations were adopted to predict the rolling forces and torques required for the rolling process. The rolling torque required for the case of 28% vertical compression rate is 73% higher than the case of 12% compression rate. The curve fittings of the rolling torque and the compression force with respect to the compression rate were obtained with very high R-square values (0.99 and 0.98) in the first rolling pass. The rolling force required for the Bézier curve groove-shape design is no different compared to the oval design with the same compression rate, but the rolling torque requirement for the next rolling station is 6% less than the oval groove design. Furthermore, the equivalent strain distribution on the cross section of the product was uniform, and no fin flash defects occurred. The proposed Bézier curve groove-shape is a better design from the viewpoint of uniform product mechanical property requirement, and a larger compression rate per pass could be achieved.

Microstructure evolution and process optimization of molybdenum rods during loose tooling forging

Defects such as abnormal grain growth and cracking are easy to occur in the process of loose tooling forging of large-size molybdenum rods prepared by powder metallurgy. In this work, the forging process of molybdenum rods was simulated, which were heated to 1350 °C, and one end of them was subjected to loose tooling forging with deformation of 20%, 30% and 40%, and then they were subjected to secondary heating at 1200 °C, 1250 °C, 1300 °C and 1350 °C for 60 min. The microstructure of the molybdenum rods was characterized by optical microscope (OM), and the equivalent stress, equivalent strain and damage distribution characteristics of during the forging process were calculated by Deform-3D finite element software. The microstructure evolution law and crack formation mechanism during deformation were analyzed. The results show that when the two ends of the molybdenum rods were separately forged and heated, incomplete static recrystallization was easy to occur in the middle gradient deformation zone due to the uneven distribution of stress and strain, resulting in the abnormal growth of local grains. In the subsequent forging process, the surface of the molybdenum rods was cracked due to the excessive stress at the grain boundary of the coarse grains in the transition zone. The initial temperature and softening temperature of static recrystallization in tempering process were different with the deformation of molybdenum rods. Finally, the process optimization of molybdenum rods forging was put forward.

Experimental and numerical investigation of severe plastic deformation of copper sheets processed by modified-constrained studded pressing

In this study, mechanical behavior and microstructural evolution of copper sheets, produced by modified-constrained studded pressing (modified-CSP) as a severe plastic deformation (SPD) method, were investigated by experimental and numerical methods. A finite element model (FEM) was established to analyze distribution of equivalent total strain, distribution of equivalent plastic strain and residual stress for the complete first pass of the process. Local stress concentration was predicted by FEM. Also, copper sheets were deformed by the modified-CSP from the first to the tenth passes. The distribution of residual stress on the surface of the copper sheets was measured at each step of the process. Crack initiation and propagation were investigated by the non-destructive penetration test (PT). The residual stresses were predicted by X-ray diffraction (XRD) via sin2 Ψ method. The residual stresses were determined for the annealed and the first pass samples, +128.2 and +80.4 MPa, respectively. The maximum compression residual stress was −62.5 MPa for the tenth pass sample. The microstructural evolution including grain size and dislocation density of samples during the process were investigated by XRD pattern analysis. The average grain size had a significant decrease from ∼35 to ∼76 nm for annealed sample and tenth pass of modified-CSP, respectively.

A unified model of ductile fracture considering strain rate and temperature under the complex stress states

In the thermoforming process of complex components, such as the multi-directional loading forming of multi-cavity parts, complex stress states always exist and change. Meanwhile ductile fracture is prone to occurring, which is sensitive to stress state, as well as deformation temperature and strain rate. This makes fracture behavior very complex and prediction for it difficult. In this paper, a new type of fracture test device was developed, also a trapezoidal groove shape (TGS) specimen was ingeniously designed to change the stress state from tension-shear to pure shear and compression-shear only by increasing the groove bridge angle β. The fracture behaviors of AA7075-H112 under strain states 0.04s−1∼1s−1 and temperatures 20 °C∼450 °C were studied, and the fracture mechanism was identified as a mixture of surface shear and core tensile fracture, but an increasing β promoted the formation and proportion of shear plane and finally led to shear fracture. Based on this, a shear-dominated DF2014 model was determined as the basic framework, then the temperature and strain rate terms of Johnson-Cook fracture model were referenced and modified to be introduced, and finally a unified thermoforming fracture model under various complex stress states was established. The full set of model parameters was determined by a hybrid experimental-numerical method and the predictions of model were verified to match the experimental ones. Then the distribution of critical equivalent strains to fracture was presented in space of stress triaxiality and Lode parameter, which showed a good predictive capability over a wide stress state range with low stress triaxialities.

Effect of equal channel angular pressing on microstructure evolution and properties variations of a CuCrZrY alloy

The microstructural evolutions and properties variations of a CuCrZrY alloy processed by equal channel angular pressing (ECAP) with different passes were studied systematically. After 4 passes of ECAP, the average grain size was decreased to 500 nm, and the grain size distribution became more uniform during the subsequent processing. After 8 passes ECAP-ed and aged at 400 °C for 7 h, the samples’ tensile strength and electrical conductivity are 560 MPa and 86.4%IACS. The main strengthening mechanisms are precipitation strengthening, low-angle grain boundary strengthening, and high-angle grain boundary strengthening (about 82% in total). Finite element simulation was carried out through ABAQUS to obtain the equivalent strain distribution diagram of ECAP, resulting in that the strain force of the outer region was less than that of the inner one. The inconsistency of deformation leads to the inhomogeneity of microstructure. These findings will effectively guide researchers to develop high-strength high-electrical conductivity copper alloys.

Three-dimensional fluid-thermal-structure multiphysics interaction simulation model of aluminium extrusion process

Three dimensional fluid-thermal-structure multiphysics interaction simulation model of aluminium extrusion process has been simulated and presented in this paper. This multiphysics complex geometrical engineering process is simulated effectively using computational fluid dynamics (CFD) simulation with very high accuracy, where the aluminium material is treated as a fluid that has a very high viscosity which depends on temperature and velocity. When aluminium moving, the inner friction will work as a heat source, therefore the model of the heat transfer is completely coupled together with those governing model of the fluid dynamics. Material properties come into a viscosity function that can be related to the flow stress locally depending on forming velocity and temperature. In addition, the stresses distribution in the die that introduces due to the fluid pressure and the thermal loads has been modelled by fully coupled the simulation model with the structural mechanic's analysis. Fully three-dimensional results during the process of the temperature distribution, velocity profile, von Mises stress distribution, total displacement and deflection distribution, equivalent volumetric strain distribution, and pressure distribution are presented and analysed with a focus on the fundamental understanding. The model is shown to be able to provide a computer-aided design tool for optimize this complex engineering process by improving productivity and reducing scrap.

Self-bending extrusion molding of distorted channels

Using an integrated profile extrusion and bending forming process with a streamlined extrusion die, a new self-bending extrusion molding technology is proposed with an axis-distorted variable channel. By designing the streamlined extrusion die structure of the distorted central axis, the metal was made to flow non-uniformly in the die cavity, thereby directly extruding a bent profile. The central axis of the streamlined extrusion die is described by a trigonometric function and a Gaussian function. A numerical simulation was applied to analyze the metal flow pattern, equivalent strain, and strain-rate distribution during the self-bending extrusion process. The influences of the extrusion velocity and the addition of a bearing on the self-bending deformation profiles were investigated. During the extrusion process, the streamline at the center of the billet could describe the overall flow of the metal in the die cavity, and the distance between the point on the end face of the die outlet and the center of the die outlet directly determined the degree of extrusion and bending. The greater the distance was, the larger was the degree of bending. The metal strain on the convex edge of the die was greater than that on the concave edge of the die, with the extruded profile always bending toward the concave edge. The strain rate of the metal changed the fastest near the most convex point of the die. As the extrusion velocity increased or more bearings were added, the radius of curvature of the extruded profile increased nonlinearly.

Effects of premature contact in maxillary alveolar bone in rats: relationship between experimental analyses and a micro scale FEA computational simulation study.

The aim of the investigation was to evaluate the maxillary alveolar bone morphology, bone architecture, and bone turnover in relation to the mechanical strain distribution in rats with dental premature contact. Fifty 2-month-old male Wistar rats were used. The premature contact group (N=40) received a unilateral (right side) resin cementation on the occlusal surface of the upper first molar. The animals were distributed in 4 subgroups according to the periods of euthanasia: 7, 14, 21, and 28 days after cementation (N=10, for each period). For the control group (N=10), the teeth were kept without resin, featuring a normal occlusion. The pieces including the upper first molars, alveolar bone, and periodontal tissue were processed to histological and immunohistochemical evaluation of RANK-L and TRAP protein expression. A three-dimensional bone microarchitecture analysis was performed, where the heads of animals were scanned using microtomography and analyzed using CT-Analyser software (Bruker, Kontich, Belgium). In the computer simulation by finite element analysis, two micro-scaled three-dimensional finite element models of first molar and dentoalveolar tissues were constructed, in representation of control and premature contact groups, using Materialise MIMICS Academic Research v18 (Materialise, Leuven, Belgium). The analysis was set to simulate a maxillary molar biting during the power stroke phase. The total deformation, equivalent strain, and minimum principal strain distribution were calculated. The expression of RANK-L and TRAP presented higher positive ratio in the 7-day period compared to the control group. The three-dimensional morphometry showed decrease of bone volume in the premature contact, with significant values between the control and the 7-day and 14-day groups (P = 0.007). In FEA, the premature contact model presented a uniform compressive strain distribution in the alveolar bone crest compared to a non-uniform compressive strain distribution in the control model. The results from FEA, 3D bone microarchitecture, and histological and immunohistochemical analyses showed that a model with dental traumatic occlusion resulted in changes of alveolar bone mechanobiology and, consequently, its morphology. These results could be applied in dental treatment planning bringing biological and mechanical feedback to provide an effective mechanism to obtain physiological bone loss responses. Furthermore, this association between experimental and computational analyses will be important to figure out the alveolar bone response to mechanical stimulation in different clinical conditions.

Strengthening effect of laser shock peening on 7075-T6 aviation aluminum alloy

The strengthening effect and uniformity of residual stress and strain of 7075-T6 aviation aluminum after laser shock peening were investigated. The finite element simulation model of laser shot peening on 7075-T6 aviation aluminum alloy was established and verified. On this basis and combined with experiment, the microstructure, residual stress distribution and equivalent strain distribution of 7075-T6 aviation aluminum alloy after laser shock peening were studied. An index U for evaluating the strain uniformity in the peened area was proposed based on the statistical processing of the equivalent strain distribution in the peened area. The results show that the average grain size on the peened surface of the specimen was refined to 20–30 μm after LSP, and a residual compressive stress layer with thickness of about 0.5 mm was induced on the surface. Grain refinement and residual compressive stress can promote the strength and fatigue properties of 7075-T6 aviation aluminum alloy. The minimum value of U is obtained in the 6 × 6 spot array (the corresponding overlap ratio is 58%), which suggest that the most uniform deformation peened area can be obtained by using 58% overlap ratio in the laser shot peening process, which can avoid stress concentration and improve fatigue life.

Feasibility Analysis of Cross Wedge Rolling (CWR) of Hexahedral Billet

In order to expand the product range of cross wedge rolling (CWR) and realize the CWR of hexahedral billet, the hexahedral CWR is studied. In this paper, a three-dimensional finite element model (FEM) of hexahedral cross wedge rolling is established by using DEFORM software. In this paper, a three-dimensional FEM of hexahedral CWR is established by using DEFORM finite element software. The change and distribution of equivalent stress and strain in the rolling process of hexahedral billets are analyzed. By tracking the strain in the rolling core of hexahedral billet, the change law of strain in each stage of forming process is obtained. The equivalent strain during the manufacturing process, the obtained CWR of hexahedral billet and round billet are basically the same. The feasibility of CWR of hexahedral billet is further verified by experiments. The research results provide theoretical guidance for realizing CWR of hexahedral billet.

Cross-section deformation behaviors of a thin-walled rectangular tube of continuous varying radii in the free bending technology

Abstract Thin-walled rectangular tube bent parts of continuous varying radii are widely used in aircraft, aerospace, aviation, radar, and several high-tech industries to save space and satisfy the internal structure compact of the specific products. In the previous years, the applications of thin-walled rectangular tubes were hindered because of the distortion in the cross-section area, which occurred during deformation. Nevertheless, due to its unique characteristic, free bending technology is highly suitable to form tubular components with a variable bending radii and bends in several planes. Thus, in this study, the deformation behavior of a thin-walled tube (with a rectangular cross-section area) of continuous varying radii during free bending technology was investigated. Besides, a stress analysis model was proposed to predict the equivalent stress and strain distribution. The proposed model was verified using simulations and experimentation. Furthermore, the influence of two key parameters (feeding speed and fillet radius) on the formability of a thin-walled rectangular tube was discussed. The remarkable results obtained from this study verify that free bending technology is a significant forming technology to manufacture rectangular thin-walled tubes with continuous varying radii.

Application of pre-deformation rolling in the welding heat-affected zone of tailor-welded blanks formed by deep-drawing process

Excessive wall thickness reduction occurs in the welding heat-affected zone (HAZ) of tailor-welded blanks (TWBs) during the deep-drawing process. The pre-deformation rolling (PDR) for welding HAZ was introduced in this study. The double-ellipsoidal heat source mechanical model was used to simulate welding, PDR, and plastic deformation processes of standard tensile specimens and large-size TWBs. Results show the uniform distribution of equivalent strain and wall thickness of the specimens with 4 % PDR reduction in the HAZ after uniaxial tensile deformation under the same elongation. Thus, the 4 % rolling reduction not only improves the material strength of the HAZ but also ensures good ductility. The optimum 4 % PDR parameters are applied to the deep-drawing process of large TWB container heads. The wall thickness of the HAZ and the base material are uniformly reduced after the deep drawing of the TWB because 4 % PDR improved the plastic deformation capability of the HAZ. Finally, the experimental study on the deep drawing forming and microstructure of large TWBs is conducted. Compared with the HAZ without PDR, the HAZ wall thickness of the deep-drawing forming head with 4 % PDR reduction in the HAZ is increased from 3.98 mm to 4.25 m. Moreover, the grains are fine and uniform similar to those of the base material. Furthermore, the distribution of hardness values in each area of the deep-drawing formed head is uniform.

Through-Thickness Microstructure and Strain Distribution in Steel Sheets Rolled in a Large-Diameter Rolling Process

The rolling condition for fabricating a low-carbon niobium-microalloyed steel sheet with an ultrafine-grained (UFG) structure was examined through rolling experiments and finite element analysis. A large-diameter rolling process was proposed to create a UFG structure. The rolling was conducted near the transformation point, Ar3, from austenite to ferrite. The Ar3 was measured at the surface and the center of the sheet. First, the through-thickness microstructure and equivalent strain distribution in a 1-pass rolled sheet 2.0 mm thick were examined. In the rolling experiments, the embedded pin method was employed to understand through-thickness deformation. The magnitude of the equivalent strain to obtain a UFG structure was estimated to be 2.0. Based on these results, the fabrication of a 2 mm UFG steel sheet by 3-pass rolling for an initial thickness of 14.5 mm was attempted by the proposed large-diameter rolling process.