Average Plastic Strain Research Articles

Dynamic response of single-layer reticulated shell with explosion-protection wall under blast loading

To investigate the structural dynamic response of long span reticulated shell under external blast loading considering explosion-protection wall, explicit finite element (FE) programme LS-DYNA is used to set up the analytical model of explosion-protection wall corresponding to an experiment to grasp the propagation law of blast shock waves around the wall. The results of simulation and experiment are compared and the results verify the creditability and applicability of numerical simulation by using ALE (Arbitrary-Lagrange-Euler) algorithm. A Kiewitt8 single-layer reticulated shell of refinement with span of 40 m is established to simulate the responses of structure considering explosion-protection wall, which contains reticulated shell member, purlin hanger, purlin, rivet and roof boarding. According to simulation results from the maximum nodal displacement, average plastic strain and yielding degree of cross section of reticulated shell member, the dynamic response laws are proposed based on varying parameters, including height, position, length, material of the explosion-protection wall, rise-span ratio of reticulated shell and TNT explosive weights. Meanwhile, the influence rules of explosion-protection wall and structure on diffraction and reflection action of blast shock wave are obtained. In addition, the adverse height of the explosion-protection wall for reticulated shell with span of 40 m under external blast loading is proposed. Four damage types of reticulated shell with the explosion-protection wall subject to external blast loading are defined by summarizing all the structural response of FE numerical models, which could provide reference for reasonable explosion-proof design for reticulated shell structure.

Texture evolution of annealed Fe-19Cr-2Mo-Nb-Ti ferritic stainless steel

Texture evolution of Fe-19Cr-2Mo-Nb-Ti ferritic stainless steel was investigated under different annealing temperatures. After cold rolling, the in-grain shear bands provide more recrystallization nucleation sites to {111} recrystallization grains with high Taylor factor during recrystallization. As the annealing temperatures increase, the average size of annealed grains and precipitates gradually increase, and 1050 °C annealed grains are dominated by the uniform and equiaxial {111} recrystallization grains favourable for the formability. Accordingly, as the annealing temperatures increase, the average plastic strain ratio of annealed sheets rises to 1.71 monotonically.

Strain energy based low cycle fatigue damage analysis in a plain C-Mn rail steel

Strain-controlled low cycle fatigue tests were performed on 60kg/m 90-UTS plain C-Mn rail steel with fully pearlitic microstructure. Analysis of hysteresis loop shape and properties revealed that the steel deviated from the ideal Masing type material behaviour to a little extent. To evaluate the fatigue damage in rail steel, energy-based analytical approach proposed by Morrow based on Masing hypothesis was employed. The Morrow energy model resulted in reasonably good approximation of both average plastic strain energy and fatigue life in comparison to experimentally observed values. In addition to that the plastic strain energy density (ΔWp) was correlated to fatigue life (2Nf) through a simple power law and very well represented by Coffin-Mansion type relationship similar to conventional strain-life (Δεp – 2Nf) relationship. Finally, the concept of fatigue toughness, an energy parameter, was introduced to life prediction in rail steel which was proved to be a suitable and reliable alternative to strain-life approach in fatigue damage evaluation with high degree of accuracy.

Flow and fracture behavior of aluminum alloy 6082-T6 at different tensile strain rates and triaxialities.

This study aims to investigate the flow and fracture behavior of aluminum alloy 6082-T6 (AA6082-T6) at different strain rates and triaxialities. Two groups of Charpy impact tests were carried out to further investigate its dynamic impact fracture property. A series of tensile tests and numerical simulations based on finite element analysis (FEA) were performed. Experimental data on smooth specimens under various strain rates ranging from 0.0001~3400 s-1 shows that AA6082-T6 is rather insensitive to strain rates in general. However, clear rate sensitivity was observed in the range of 0.001~1 s-1 while such a characteristic is counteracted by the adiabatic heating of specimens under high strain rates. A Johnson-Cook constitutive model was proposed based on tensile tests at different strain rates. In this study, the average stress triaxiality and equivalent plastic strain at facture obtained from numerical simulations were used for the calibration of J-C fracture model. Both of the J-C constitutive model and fracture model were employed in numerical simulations and the results was compared with experimental results. The calibrated J-C fracture model exhibits higher accuracy than the J-C fracture model obtained by the common method in predicting the fracture behavior of AA6082-T6. Finally, the Scanning Electron Microscope (SEM) of fractured specimens with different initial stress triaxialities were analyzed. The magnified fractographs indicate that high initial stress triaxiality likely results in dimple fracture.

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.

Effect of different cyclic expansion–extrusion processes on microstructure and mechanical properties of AZ80 magnesium alloy

In this work, cyclic expansion–extrusion process in the same plane and cyclic expansion–extrusion process in two orthogonal planes have been employed, and the isothermal finite element simulations of both processes have been carried out. The equivalent plastic strains of AZ80 magnesium alloy billets produced by cyclic expansion–extrusion process in the same plane and cyclic expansion–extrusion process in two orthogonal planes were analyzed. Furthermore, the distinction between the accumulated equivalent plastic strains of both processes was also explored. The AZ80 magnesium alloy samples machined from the deformed billets were tested by tensile test machine, hardness tester, and optical microscope. This work also discussed the relationships between the microstructure and mechanical properties of deformed billets. The research results show that the average equivalent plastic strain of deformed billet is larger caused by two-pass cyclic expansion–extrusion process in two orthogonal planes than that by two-pass cyclic expansion–extrusion process in the same plane, and furthermore, the deformation uniformity after two-pass cyclic expansion–extrusion process in two orthogonal planes is far superior to that after two-pass cyclic expansion–extrusion process in the same plane. Cyclic expansion–extrusion process in the same plane can partly refine the grain size of annealed alloy from 190 to around 10 µm; however, cyclic expansion–extrusion process in two orthogonal planes can substantially refine that from 190 to approximately 3 µm. Two-pass cyclic expansion–extrusion process in the same plane can significantly improve the Brinell hardness of annealed alloy from 61.5 to 88.5 HB. Similarly, two-pass cyclic expansion–extrusion process in two orthogonal planes can also obviously improve that from 61.5 to 86.6 HB. Ultimate tensile strengths via two-pass cyclic expansion–extrusion process in the same plane and cyclic expansion–extrusion process in two orthogonal planes increase by 60 and 40 MPa than the annealed alloy, respectively. With the identical strain accumulation and deformation temperature, cyclic expansion–extrusion process in two orthogonal planes might look to be attractive when compared with equal-channel angular pressing for improvement of ultimate tensile strength and hardness as well as for grain refinement.

Depth-sensing cyclic nanoindentation of tantalum

In the present paper, depth-sensing multi-cycling instrumented indentation testing of tantalum is studied to assess depth-dependent plastic deformation of the metal at room temperature. Loading/unloading/reloading scheme in cyclic indentation testing is a reliable indentation-based approach in which data collection is not necessarily adversely affected by lateral in-homogeneities of the sample leading to more accurate measurements. The experimental results show indentation size effect (ISE) and depth-dependent strain rate sensitivity in Ta. To interpret these phenomena, the density of geometrically necessary dislocations (GNDs) and statistically stored dislocations (SSDs) constructed by the Nix-Gao model were used. The observed dependence of hardness and activation volume upon indentation depth indicated that the average flow stress, and hence the average plastic strain, is higher around the small indentations than around the deep indentations.

Quantification analysis of the heterogeneity of microstructure of dual phase steel

Requirements for weight reduction and increased formability in the automotive industry have largely contributed to the development of dual phase (DP) steels, which is a widespreadly kind of high strength steels. Due to the microstructural of dual phase (DP) steels consisting of hard martensite dispersed in a soft ferrite matrix and with different mechanical behaviors of the two phases, the inhomogeneous deformation of the microstructure are generated during the plastic deformation process. In this study, the strain distribution and plastic strain gradient of microstructure is obtained by Point Interpolation Method (PIM). The PIM interpolates a cluster of feature data points to construct its shape function to attain the displacement increments, which shows great convenience and certain precision in computing the strain and gradient distribution of individual phases. A nonlinear function is developed to describe the relationship of individual phases strain and overall material strain. The overall strain of material is greater than the strain of martensite and less than ferrite’s. Considering the different stain value of the two phases during the deformation process, the plastic strain gradient is generated to connect the inhomogeneous deformation in the two phases to ensure the deformation compatibility. The average plastic strain gradient is the second derivative of the deformation field of microstructure. The average plastic strain gradient of both phases is built with a power function of overall strain. The results show that greater strain gradient value in martensite phase than ferrite. The effects of grain size on the plastic strain and strain gradient have been studied in this paper. The both of plastic strain and strain gradient of ferrite increase with decreasing of grain size. The grain size has greater impact on strain gradient than plastic strain. The rules of martensite are similar to ferrite and the effects of grain size on martensite are less than ferrite. The grain size plays a critical role in plastic strain and strain gradient of dual phase steel.

Ultrasonic elliptical vibration cutting of hard materials: simulation and experimental study

In this paper, orthogonal cutting experiments and a simulation analysis of ultrasonic elliptical vibration cutting (UEVC) of hard material were performed by adopting a resonant UEVC actuator. The effects of the cutting regime parameters (ultrasonic elliptical vibration excitation, cutting speed, crossfeed, and depth of cut) on the cutting resistance, chip morphology, and surface integrity during the UEVC process were experimentally investigated. The von Mises stress distribution in the primary deformation zone in one ultrasonic elliptical vibration cycle was used to describe the cutting nature of UEVC. It was also shown through both analysis and experiments that the cutting resistance in UEVC is lower as compared to conventional cutting. At last, the different nature of the chip formation mechanisms in the two processes were also analyzed through a free body force analysis of the chip. The chip shapes from experiments and finite element analysis (FEA) are compared and discussed based on the average equivalent plastic strain in the chip.

Improvement in Plastic Strain Ratio of AA1050 Al Alloy Sheet by Enhancing the <111>//ND Texture Component

The average plastic strain ratio (the R-value) and the anisotropy parameter |ΔR| calculated from the measured texture of AA1050 Al alloy sheet treated by the heavy asymmetric rolling by 84% reduction in thickness and subsequent annealing for 1 h at 500 °C, followed by light rolling by 10% or 20% reduction in thickness and the subsequent annealing for 1 h at 500 °C increased by 1.52 times that of the non-processed specimen and reduced to 1/12 times that of the non-processed specimen, respectively.

Effect of Annealing Time on the Formability of a Ultra Purified Ferritic Stainless Steel Containing Copper

For developing of a ultra-purified ferritic anti-bacterial stainless steel, 1.4 Cu % was added in 21% Cr ferritic stainless steel. The effect of annealing time on the formability was analyzed. The micro texture of steel was measured by using electron back scattering diffraction analysis. The Cu precipitates through different annealing periods were investigated by means of transmission electron microscopy. Average plastic strain ratio was calculated by the r values at 0, 45°and 90° directions measured by tensile testing. The results shows that with the extension of annealing time, the morphology of the Cu precipitates became into rod from spherical and the size increased. Average plastic strain ratio increased first and then decreased, while the change trend of anisotropy index was opposite. The higher formability is due to the {111} texture components increase significantly, while more {001}<110> component at 60 min was adverse for the formability. And anisotropy index was determined by γ components and {110}<110> components.

A Shear-Tension Specimen for Large Strain Testing

A new shear-tension specimen (STS) is designed, evaluated and tested quasi-statically and dynamically. The specimen consists of a long cylinder having an inclined gauge section created by two diametrically opposed semi-circular slots which are machined at 45° with respect to the longitudinal axis. The geometry imposes stress condition within the gauge section which correspond to a Lode parameter of ~ −0.5, between pure shear (0) and uniaxial tension (−1). It thus provides a wider span of loading conditions for a material. A thorough numerical study reveals that the stresses and strains within the gauge are rather uniform, and the average Mises stress and plastic strain on the mid-section of the gauge represent the material true stress–strain characteristics. The data reduction technique to determine the stresses and strains is presented. Quasi-static and dynamic tests at strain rate of 104 1/s were carried out on specimens made of 1020 cold-rolled steel. No necking or softening was observed with this specimen, and the fracture location was always well within the gauge. The obtained stress–strain curves and ductility were validated numerically. The STS is a new specimen to study the combined influence of tension and shear on the mechanical characteristics of a material.

Structure and Properties of Kh20N80 Alloy Powders Produced by Impact Sintering at Different Temperatures

The compaction, structure, and mechanical properties of Kh20N80 powder samples are studied. Most of the powder particles were 25 μm in size. The powders were compacted by impact sintering in vacuum at 1100, 1150, 1200, 1250, and 1300°C at an impact energy of 1200 J/cm 3 . Isothermal holding at these temperatures lasted for 20 min, vacuum during heating and compaction was maintained at 0.013 Pa, and initial strain rate was 6.5 m/sec. The rectangular bars cut out of cylindrical disks were used to determine the density, electrical resistivity, tensile strength, fracture toughness or fracture work of a notched sample, Brinell hardness, compression strength, and plasticity of the samples in various test conditions. It is shown that the mechanical properties of Kh20N80 samples subjected to impact sintering at 1100–1300°C correspond to those of standard Kh20N80 alloy obtained by conventional melting and forging techniques. In particular, the average tensile strength varies from 630 to 740 MPa and compression strength from 800 to 830 MPa. The plasticity of the samples evaluated from necking changes from 30 to 54% with compaction temperature increasing from 1100 to 1300°C. The average plastic strain energy at break of a notched sample increases from 19.5 to 36.0 J/cm 2 .

A Modified Closed Form Energy Based Framework for Axial Isothermal-Mechanical Fatigue Life Assessment for Aluminum 6061-T6

In the present investigation, the applicability of a previously developed closed form energy based framework to predict low cycle fatigue (LCF) life of aluminum 6061-T6 was extended from room temperature to elevated temperature. The three different elevated temperatures considered in the present investigation were 75 °C, 100 °C, and 125 °C which were below the creep activation temperature for aluminum 6061-T6. Like the room temperature life assessment framework, the elevated temperature life assessment framework involved computation of the Ramberg–Osgood cyclic parameters from the average plastic strain range and the average plastic energy obtained from an axial isothermal-mechanical fatigue (IMF) test. The temperature dependent cyclic parameters were computed for 25 °C (room temperature), 75 °C, and 100 °C and then extrapolated to 125 °C utilizing functions describing the dependence of the cyclic parameters on temperature. For aluminum 6061-T6, the cyclic parameters were found to decrease with increase of temperature in a quadratic fashion. Furthermore, the present energy based axial IMF framework was found to be able to predict the LCF life of aluminum 6061-T6 at both room and elevated temperatures with excellent accuracy.

A Modified Closed Form Energy Based Framework for Fatigue Life Assessment for Aluminum 6061-T6—Damaging Energy Approach

A previously developed energy based high cycle fatigue (HCF) life assessment framework is modified to predict the low cycle fatigue (LCF) life of aluminum 6061-T6. The fatigue life assessment model of this modified framework is formulated in a closed form expression by incorporating the Ramberg–Osgood constitutive relationship. The modified framework is composed of the following entities: (1) assessment of the average strain energy density and the average plastic strain range developed in aluminum 6061-T6 during a fatigue test conducting at the ideal frequency for optimum energy calculation, and (2) determination of the Ramberg–Osgood cyclic parameters for aluminum 6061-T6 from the average strain energy density and the average plastic strain range. By this framework, the applied stress range is related to the fatigue life by a power law whose parameters are functions of the fatigue toughness and the cyclic parameters. The predicted fatigue lives are found to be in a good agreement with the experimental data.

Distortion Measurement of Ship Blocks Using Photogrammetry

Welding being a transient phenomenon, explicit finite element thermomechanical analysis of large structural units is computationally extremely time-consuming and in general not feasible. Computational methods are available; however, they need to be validated with full-scale shop floor measured data. As of now, it is extremely difficult to do measurements and acquire some tangible data in actual shop floor situation. In the present work, a method was proposed to actually get the dimensions of such large structures through the use of multiple digital photographs of the structure. The photographs were then processed through a software to get to the dimensions of the three-dimensional structure. For validating this method of measurement, two test cases were undertaken. First was using a flat surface plate measuring 3.3 m × 1.3 m over which black dots were pasted at predetermined positions. The distances between the dots were measured using a laser distance meter and compared with those obtained through photogrammetry. In the second case, a test sample was fabricated using a 500 m × 500 mm, 8-mm thick mild steel plate and two longitudinal and one transverse stiffener of 75 × 50 × 6 angle sections. Photographs were taken both before and after welding of the stiffeners. This set of photographs was processed to obtain the resulting deformation of the plate resulting from welding of the stiffeners. The distortion obtained through photogrammetry was compared with the distortion shape of the welded panel obtained from finite element analysis using an average plastic strain method. In both cases, the results of photogrammetry compared fairly well with those of laser distance meter measurements and finite element analysis. The proposed method shows great promise toward actual measurement of large blocks of ship structures and thereby satisfactorily validating theoretical methods of distortion prediction of such large structures.

Distortion Measurement of Ship Blocks Using Photogrammetry

Welding being a transient phenomenon, explicit finite element thermomechanical analysis of large structural units is computationally extremely time-consuming and in general not feasible. Computational methods are available; however, they need to be validated with full-scale shop floor measured data. As of now, it is extremely difficult to do measurements and acquire some tangible data in actual shop floor situation. In the present work, a method was proposed to actually get the dimensions of such large structures through the use of multiple digital photographs of the structure. The photographs were then processed through a software to get to the dimensions of the threedimensional structure. For validating this method of measurement, two test cases were undertaken. First was using a flat surface plate measuring 3.3 m ×1.3 m over which black dots were pasted at predetermined positions. The distances between the dots were measured using a laser distance meter and compared with those obtained through photogrammetry. In the second case, a test sample was fabricated using a 500 m × 500 mm, 8-mm thick mild steel plate and two longitudinal and one transverse stiffener of 75 × 50 × 6 angle sections. Photographs were taken both before and after welding of the stiffeners. This set of photographs was processed to obtain the resulting deformation of the plate resulting from welding of the stiffeners. The distortion obtained through photogrammetry was compared with the distortion shape of the welded panel obtained from finite element analysis using an average plastic strain method. In both cases, the results of photogrammetry compared fairly well with those of laser distance meter measurements and finite element analysis. The proposed method shows great promise toward actual measurement of large blocks of ship structures and thereby satisfactorily validating theoretical methods of distortion prediction of such large structures.

2단계 비대칭 압연과 열처리한 AA5083 Al 합금판재의 집합조직과 소성변형비 변화

The plastic strain ratio is one of the factors that affect the deep drawability of Al alloy sheet. The deep drawability of Al alloy sheet is limited because of its low plastic strain ratio. Therefore an increase in the plastic strain ratio to improve the deep drawability of Al alloy sheet is needed. The current study investigated the increase of the plastic strain ratio and the change in texture of AA5083 Al alloy sheet after a 2 step asymmetric rolling with heat treatments. The average plastic strain ratio of initial AA5083 Al alloy sheets was 0.83. After the first asymmetric rolling step of 88% deformation and subsequent heat treatment at 320°C for 10 minutes the value was still 0.83. After the second asymmetric rolling of 14% reduction and subsequent heat treatment at 330°C for 10 minutes the plastic strain ratio rose to 1.01. The average plastic strain ratio after the 2 step asymmetric rolling and heat treatment is 1.2 times higher than that of initial AA5083 Al alloy sheet. This result is related to the development of ND/ texture component after the second asymmetric rolling and heat treatment.

Modelling the effect of elastic and plastic anisotropies on stresses at grain boundaries

It is believed that intergranular stresses play a significant role in failure processes, such as stress corrosion cracking (SCC) and fatigue cracking. In deformed cubic metals, intergranular stresses arise solely from the plastic and elastic anisotropies of the individual grains. In this work, stresses normal to the grain boundaries in deformed stainless steel have been calculated using crystal plasticity finite element modelling (CPFEM). The calculations show that, at strains larger than 0.5% and under load, the stress at grain boundaries is dominated by the effect of plastic anisotropy rather than elastic anisotropy. Upon unloading, plastic misfit still fully dominates the heterogeneity of normal stresses and is insensitive to the angle between the boundary normal and the preloaded direction. The effects of mesh density and size of boundaries on normal stresses are also studied. Special attention has been focused on examining what conditions give rise to large grain boundary stresses. Our results suggest that the magnitudes of the predicted residual grain boundary stresses are not highly correlated to the amount of plastic strain in the vicinity of the boundary and whether it is higher or lower than the average plastic strain. In other words, a soft-hard grain combination does not imply high tensile (nor compressive) residual stress normal to its boundary. The results are similar if instead of comparing the plastic strain near neighbours, we compare the plastic strain in the grain to the average plastic strain.

Effect of Heat Treatment Processes on Microstructure and Mechanical Properties of Nb-Ti-Stabilized 430 Stainless Steel Plate

In this research, influence of annealing process on microstructure and mechanical performance of Nb-Ti-stabilized 430 ferritic stainless steel were investigated. In order to obtain the optimal annealing process, metallographic observation, SEM detection and tensile test were carried out. It is found that the microscopic structure is composed of fine and uniform isometric recrystallization grain after annealing. Optimum microstructure and mechanical properties can be achieved while annealed at 950 °Cfor 90 seconds. The annealed sample can obtain the optimum microstructure and mechanical properties under such annealing process. The yield platform is eliminated and the average plastic strain ratio is further improved to 1.269, which reflected a well deep drawability of the Nb-Ti-stabilized 430 ferritic stainless steel compared to SUS 430 stainless steel.