Elastic-plastic Region Research Articles

Prediction of fatigue crack propagation behavior in elastic plastic region under block loading for type 316 steel via artificial neural network approach

This study investigated the fatigue crack propagation behavior from small defect in the elastic–plastic region under block loading conditions and clarified the influence of cycle ratio on the crack growth rate. Fatigue tests were conducted under constant and repeated two-step strain amplitude loading conditions using various cycle ratios. The results of the constant amplitude loading test indicated that the J integral can be employed to predict fatigue crack propagation rate in one master curve by considering the material constant, l0. The results of the repeated two-step test showed that the fatigue life evaluated via the J integral had a larger scatter for test conditions at strain amplitudes of 1.0%/0.2% and 0.8%/0.2% with various cycle ratios. A highly accurate model was established to predict fatigue crack propagation behavior and investigate the effect of algorithms on the precision of models. To achieve this, three deep learning algorithms feed forward neural network (FFNN), cascade-forward neural network (CFNN) and function fitting neural network (FNN), were employed. It was observed that the precision of the constructed models was dependent on the algorithms and dataset split. The model constructed using the CFNN exhibited the highest prediction accuracy.

Modeling of Tensile Stress Distribution Considering Anisotropy of Mechanical Properties of Thin-Walled AlSi10Mg Samples Obtained by Selective Laser Melting

The work that is being presented demonstrates that there is a critical point at which the engineering stress–strain diagram’s elastic–plastic region transitions to yield and fracture stresses. This transition is demonstrated using thin-walled specimens made using selective laser melting technology from high-strength aluminum alloys (AlSi10Mg) that have undergone preliminary heat treatment. It was discovered that the strain-hardening coefficient, which was determined in the section from yield strength to fracture strength, and the critical point have a highly statistically significant association (0.83 by Spearman and 0.93 by Pearson). It was possible to derive a regression equation that connected the strain-hardening coefficient with the crucial transition point. The type of stress distribution in the elastic–plastic region changes (the Weibull distribution changes to a normal distribution) as the plasticity of the thin-walled samples increases. Additionally, the contribution of the probability density of the stress distribution described by the Cauchy distribution increases in a mode near the point at which the probability density of the fracture increases.

Poisson’s Ratio of Selected Metallic Materials in the Elastic–Plastic Region

Poisson’s ratio is one of the fundamental characteristics in the material models that are used. In engineering practice, its values are assumed to be constant in the elastic and in the plastic region. In this paper, the conventionally used values of this number for steel materials and aluminum alloys are confronted with experimental results. By using non-contact strain measurements with the DIC (digital image correlation) method, the evolution of the Poisson ratio value in the regions of transition from the elastic to the plastic region as well as in the regions of large plastic deformations was documented. The obtained experimental results are graphically compared using the proposed strain scaling. The gradient of the Poisson ratio changes in the vicinity of the yield stress is significant, indicating the need for a refinement of the material models in this region. Deviations from the conventionally used value of this number were found in the large plastic deformation region. In conclusion, a possible approach for improving the accuracy of simulations in FEM softwares was formulated.

Intergranular corrosion in sensitized austenitic stainless steel subjected to tensile loading and unloading in the elastic-plastic region

This study investigates the influence of mechanical conditions on intergranular corrosion (IGC) in type 304 austenitic stainless steel. Electrochemical potentiokinetic reactivation and oxalic acid etching tests were conducted on specimens under tensile loading and unloading in the elastic-plastic region. The results show that their IGC susceptibility became higher than that of intact specimens. Furthermore, tensile loading during corrosion led to an increase in the IGC susceptibility of plastically deformed specimens. The IGC susceptibility of high-energy grain boundaries (GBs) was increased by elastic and plastic deformation around the GBs. Low-energy GBs exhibited little IGC susceptibility for all mechanical conditions.

Investigating the mechanism of splitting failure in deep high sidewall cavern based on complex function and strain gradient

Owing to excavation-induced unloading, high sidewalls of underground powerhouse are often subjected to splitting failure, which produces many adverse effects to the construction of the cavern. To reveal the formation mechanism of splitting failure, we proposed a novel elastic–plastic damage softening model based on the strain gradient theory and the elastic–plastic damage theory. Using the ODE45 program in MATLAB, the numerical solution of the displacement and stress of circular cavern was solved based on the newly proposed elastoplastic damage model. We then adopted the complex function method and used the Schwarz-Christoffel integral formula to obtain the mapping function from the outer domain of high sidewall cavern to the outer domain of the unit circle. Finally, the elastic–plastic region and the displacement distribution of high sidewall cavern were obtained by mapping the obtained elastic–plastic solution of the circular cavern under the axisymmetric condition. The numerical analysis results were consistent with the previous geomechanical model test results. The results presented that the stress of high sidewall of an underground powerhouse exhibits an oscillating variation with alternating peaks and troughs, which is the mechanical mechanism of splitting failure.

Mechanism of Splitting Failure for High Sidewall Cavern of Hydropower Station Based on Complex Function and Strain Gradient

With the rapid development of society, the number of hydropower projects has increased. During the construction of these projects, due to excavation-induced unloading, the high sidewalls of the hydropower station are often subject to splitting failure, which produces many adverse effects on the construction of the cavern. In order to reveal the formation mechanism of splitting failure of hydropower stations, based on the strain gradient theory and elasto-plastic damage theory, we proposed an elasto-plastic damage softening model. Using the ODE45 program in MATLAB, we solved the numerical solution of displacement and stress of circular cavern based on our proposed elastoplastic damage model. Then, we apply the complex function method and use the Schwarz–Christoffel integral formula to obtain the mapping function from the outer domain of the high sidewall cavern to the outer domain of the unit circle. Finally, the elastic-plastic region and displacement distribution of the high sidewall cavern are obtained by mapping the obtained elastic-plastic solution of the circular cavern under the axisymmetric condition. In future research, it is necessary to further study the corresponding relationship between the internal length parameter of the material and its internal microstructure in order to accurately determine the internal length parameter.

Elastic-plastic buckling analysis of stiffened panel subjected to global bending in forming process

A new method has been proposed in this study for the elastic-plastic buckling analysis of stiffened panels under global bending. In this method, a simplified model of the stiffened panels has been built with the application of two theories of plasticity, the incremental theory (IT) and the deformation theory (DT). The effect of transverse shear deformation through the stiffener thickness has been considered using the Mindlin-Reissner plate theory. The governing differential equations have been solved by the differential quadrature (DQ) method and an iteration process has been adopted due to the non-linearity of material properties in the elastic-plastic buckling analysis. Non-linear finite element (FE) modelling of elastic-plastic buckling analysis has been carried out, and the FE results are between those based on DT and IT in general. When the reciprocal of strain hardening exponent mt increases to 20, the FE results are in a good agreement with DT results. Based on the proposed method and FE simulations, the effect of geometric parameters of stiffened panels (stiffener thickness to height ratio, stiffened panel length to height ratio, width to height ratio, and skin thickness to stiffener thickness ratio) on buckling behaviour in the elastic-plastic region has been investigated and discussed. The proposed method provides an efficient way for parameter optimisation in the structure design of stiffened panels for the aerospace applications.

Anisotropic plasticity model forms for extruded Al 7079: Part II, validation

This is the second part of a two-part contribution on modeling of the anisotropic elastic-plastic response of aluminum 7079 from an extruded tube. Part I focused on calibrating a suite of yield and hardening functions from tension test data; Part II concentrates on evaluating those calibrations. A rectangular validation specimen with a blind hole was designed to provide heterogeneous strain fields that exercise the material anisotropy, while at the same time avoiding strain concentrations near sample edges where Digital Image Correlation (DIC) measurements are difficult to make. Specimens were extracted from the tube in four different orientations and tested in tension with stereo-DIC measurements on both sides of the specimen. Corresponding Finite Element Analysis (FEA) with calibrated isotropic (von Mises) and anisotropic (Yld2004-18p) yield functions were also conducted, and both global force-extension curves as well as full-field strains were compared between the experiments and simulations. Specifically, quantitative full-field strain error maps were computed using the DIC-leveling approach proposed by Lava et al. The specimens experienced small deviations from ideal boundary conditions in the experiments, which had a first-order effect on the results. Therefore, the actual experimental boundary conditions had to be applied to the FEA in order to make valid comparisons. The predicted global force-extension curves agreed well with the measurements overall, but were sensitive to the boundary conditions in the nonlinear regime and could not differentiate between the two yield functions. Interrogation of the strain fields both qualitatively and quantitatively showed that the Yld2004-18p model was clearly able to better describe the strain fields on the surface of the specimen compared to the von Mises model. These results justify the increased complexity of the calibration process required for the Yld2004-18p model in applications where capturing the strain field evolution accurately is important, but not if only the global force-extension response of the elastic–plastic region is of interest.

The Non-Stationary Dynamic Analytical Solution of a Spherical/Cylindrical Cavity Expansion

Abstract A review of the pertinent literature related to the dynamic expansion of a spherical/cylindrical cavity shows that all the solutions with kinematic boundary conditions deal with a constant velocity at the cavity boundary. This paper develops a new general solution of the nonstationary dynamic problem of cavity expansion, which allows the application of time-dependent motion conditions at the cavity boundary. This solution can be used, for example, in the development of approximate approaches for projectiles penetrating with a non-constant velocity into different targets. Due to the complexity of the nonlinear nonstationary problem, an analytical solution of the problem may be developed if simplified constitutive relationships are used. In the present model, a simplified material model with a locked equation of state and a linear shear failure relationship is implemented. This solution may be applied to different materials such as concrete, soil, and rock. Special cases of the newly developed nonstationary solution are compared with different spherical and cylindrical cavity expansions solutions reported in the literature, and a good agreement is obtained. The capability of the present model is demonstrated in a following investigation of representative cases of cavity expansion with zero, constant, and variable acceleration of the cavity boundary. A significant difference in the stress variation for the different cases is shown. Along with the general solution which deals with an elastic–plastic region, a simplified solution which disregards the contribution of the elastic region is presented and the evaluation of the elastic region effect may be assessed.

Improved core model of the indentation for the experimental determination of mechanical properties of elastic-plastic materials and its application

The improvement of Johnson's model (Johnson (1970), (1985)) takes into account the additional pressure and shear stresses jump at the boundary with the hydrostatic core where it is formed from the material of the elastic-plastic zone. This causes additional volumetric deformations and additional pressure in the core that increases the magnitude of the constant in the Tabor ratio. The effects of the proposed improvement of the Johnson model: additional volumetric deformations and pressure in the core, changes in the Tabor constant and related values of yield strength as well as characteristic size of the elastic-plastic region, were determined on a wide class of materials with different elastic-plastic properties. An analysis of the concept of characteristic (representative) strain is given for these materials.

Contact mechanics of elastic-plastic fractal surfaces and static friction analysis of asperity scale

PurposeThe purpose of this paper is to provide a static friction coefficient prediction model of rough contact surfaces based on the contact mechanics analysis of elastic-plastic fractal surfaces.Design/methodology/approachIn this paper, the continuous deformation stage of the multi-scale asperity is considered, i.e. asperities on joint surfaces go through three deformation stages in succession, the elastic deformation, the elastic-plastic deformation (the first elastic-plastic region and the second elastic-plastic region) and the plastic deformation, rather than the direct transition from the elastic deformation to the plastic deformation. In addition, the contact between rough metal surfaces should be the contact of three-dimensional topography, which corresponds to the fractal dimension D (2 < D < 3), not two-dimensional curves. So, in consideration of the elastic-plastic deformation mechanism of asperities and the three-dimensional topography, the contact mechanics of the elastic-plastic fractal surface is analyzed, and the static friction coefficient nonlinear prediction model of the surface is further established.FindingsThere is a boundary value between the normal load and the fractal dimension. In the range smaller than the boundary value, the normal load decreases with fractal dimension; in the range larger than the boundary value, the normal load increases with fractal dimension. Considering the elastic-plastic deformation of the asperity on the contact surface, the total normal contact load is larger than that of ignoring the elastic-plastic deformation of the asperity. There is a proper fractal dimension, which can make the static friction of the contact surface maximum; there is a negative correlation between the static friction coefficient and the fractal scale coefficient.Originality/valueIn the mechanical structure, the research and prediction of the static friction coefficient characteristics of the interface will lay a foundation for the understanding of the mechanism of friction and wear and the interaction relationship between contact surfaces from the micro asperity-scale level, which has an important engineering application value.

Atomistic-level study of the mechanical behavior of amorphous and crystalline silica nanoparticles

Molecular dynamics method was used to simulate and investigate the mechanical behavior of amorphous and crystalline silica during nanoindentation and uniaxial compression tests in the nanoscale. Also, the hardness and elastic moduli were experimentally checked by nanoindentation tests. The MD nanoindentation simulation results show that the amorphous silica has an indentation modulus less than the crystalline one, and the elastic strain of the amorphous silica is higher than crystalline silica. In contrast, the amorphous silica has a lower hardness. The uniaxial compression test results show that both structures have three deformation stages during the tests. The first stage corresponds to the linear elastic region; the second stage indicates the elastic-plastic region for crystalline silica, and yielding stage in the amorphous silica. The last stage corresponds to the fracture region for crystalline structure and densification for the amorphous structure. By comparing the area under stress-strain curves of the two structures, it can be concluded that the absorbed energy under external stress in the amorphous silica is three times greater than that in the crystalline one. Moreover, the nanoindentation tests of SPS samples made of amorphous and crystalline silica were performed, and the results confirmed that the crystalline silica has higher hardness and indentation modulus than the amorphous silica. Also, comparing the indentation moduli obtained by simulation and experimental tests shows that the indentation modulus predicted by simulation is in good agreement with that obtained based on experimental results.

Cyclic compression of a multi-layer multi-span corrugated package with plastic deformation of its tapes

In this article we present our solution of the problem of cyclic compression of a single-layer and multi-layer corrugation, as well as of a single-layer multi-span corrugation by the FEM method using Ansys. This problem can be considered as the first part of the general complex nonlinear problem of cyclic compression of a multi-layer multi-span corrugated package with dry friction on the contact surfaces. We conducted an analysis of the known published solutions to this problem, and we discovered inaccuracy of some of them and the physical reason resulting in this unacceptable error. A very large number of published solutions to this problem are generally explained by the presence of successful examples of their practical application in the field of aircraft and rocket engine manufacturing, by the wide possibilities of their use as damping devices in both of these areas, and, for example, in the automotive industry, by their high elastic-friction, strength and performance characteristics. All the known published solutions to this problem were obtained for cyclic compression of a multilayer multi-span package in the region of its elastic deformations and for the same geometric shape of the corrugation. The task of improving the mass characteristics of an engineering unit is quite relevant for the development of shock-proof single-shot damping devices that increase the passive safety of the car bumper protective devices. This can be solved by using single-layer or two-layer, multi-span packages with an optimally selected geometric shape of the corrugation, deformable in the elastic-plastic region. Therefore, the above-mentioned problems are solved taking into account the elastic-plastic deformation of the corrugations for any of their geometric shapes. The obtained solutions make it possible to construct any loading processes in the field of elastic-hysteresis package loops. We also investigated the influence of the parameters of the corrugated package on its elastic-friction characteristics (including the shape of the corrugation and the presence of gaps between the tapes of the package at the tops of their corrugations).

Probabilistic and deterministic lower-bound design benchmarks for cylindrical shells under axial compression

This article contains examples to demonstrate the use of different design concepts for cylindrical shells under axial compression. The examples are based on shells which were manufactured according to electroplating, machining, welding (isotropic cylinders) and prepreg hand layup on a mandrel (composite cylinders). Three of the four shell series are characterized by pure elastic buckling and one shell series buckled in the elastic-plastic region. All relevant data for the numerical analysis are described in the article and summarized in the Elsevier repository of this article (geometry, material, measured imperfection data and Python-ABAQUS scripts). The design concepts are based on the geometric imperfection signatures, probabilistic and deterministic lower-bound methods. The design concepts are representative for the development of design approaches for imperfection sensitive shells from the early 1980 to the late 2010 and are validated with experimental data. Recently developed design lower-bound curves for axially loaded cylinders are presented and compared with currently used design criteria like the Eurocode EN 1993-1-6 and the NASA SP-8007. The results of this article show that the design of imperfection sensitive cylinders has been significantly improved in the last 30 years.

Homogenization and localization of elastic-plastic nanoporous materials with Gurtin-Murdoch interfaces: An assessment of computational approaches

This paper critically examines the predictive capabilities of three computational approaches for the elastic-plastic response of nanoporous materials with energetic surfaces simulated with the Gurtin-Murdoch coherent interface model. These approaches involve the classical composite cylinder assemblage model, and the finite-element and generalized finite-volume homogenization theories. Exact elastic-plastic solution to the composite cylinder assemblage under axisymmetric loading is obtained analytically such that all the governing differential equations are satisfied exactly. Hence it is used as gold standard in assessing the predictive capability of the newly developed generalized finite-volume theory with surface and plasticity effects, as well as a comparable finite-element approach, under axisymmetric loading and porosity volume fractions for which pore interactions are small. The assessment includes homogenized response and local stress and plastic strain fields, as well as solution stability issues for surfaces with negative strain energies that limit the range of pore radii and volume fractions of nanoporous materials that may be analyzed. The effect of surface elasticity is shown to be magnified in the elastic-plastic region. Anomalous homogenized response that results from the use of the elastic Gurtin-Murdoch model which impacts limit surface calculations is highlighted. The generalized finite-volume theory is shown to exhibit larger range of pore radii relative to the finite-element based homogenization wherein stable solutions are obtained under both axisymmetric and asymmetric loading of hexagonal and square arrays of porosities with negative strain energies.

Linear and Non-Linear Stress Analysis for the Prediction of Fracture Toughness for Brittle and Ductile Material using ASTM E399 and ASTM E1290 By ANSYS Program package

Prediction of fracture toughness value of most the metallic materials is a very important issue to be consider in designing of engineering structural components like pipes, flow tanks and pressure vessel where it can be used in the evaluation of critical crack length that is consider very important factor in non-destructive testing because during inspections of these components, the critical crack length is being compared with the minimum allowable flow size. Fracture toughness value can be predicted by using two different types of experimental tests such as ASTM-E399 (which is used to predict fracture toughness under plane strain condition for brittle materials which undergo to small plastic deformation) and ASTM-E1290 (which is used to predict fracture toughness for ductile materials which undergo to large plastic deformation). These experimental tests utilize specimens such as compact tension specimen CT and three-point bend specimen SENB which must be pre-cracked. However, manufacturing of pre-cracked in metallic structural components before testing is expensive and time-consuming process, thus in the current study, fracture toughness will be predicted by using economized method in both time and cost that is the finite elements method by using ANSYS PROGRAM Where, a three-dimensional model has been designed by using two different types of elements (plane-82) and (solid-95).Firstly, two-dimensional model mesh will be idealized by using element type (plane-82) due to ANSYSY PROGRAM can pick–up singularity for two dimensional model only, but in order to obtain more accurate results, a three dimensional model will be designed by utilizing Sweep Model with restriction with ANSYSY abilities in the treatment of fracture mechanics problems for three dimensional model analysis where the element length must be ranging from 1to4 in all directions. In elastic region, the fracture toughness is been predicted directly from ANSAYS PROGRAM using the specification in ASTM-E-399 for compact tension specimen for practical design problems. But in elastic-plastic region, the fracture toughness is been predicted by using the crack tip opening displacement model (CTOD-Model) using the specification in ASTM-E-1290 for three-point bend specimen for practical design problem. The critical value for crack tip opening displacement will be calculated after extracting load-displacement data from ANSAYS PROGRAM then using these data in (CTOD-Model) which is separated into two components, elastic and plastic, the elastic component has been estimated using Dug Dual-Model, while the plastic component will be estimated using Plastic Hinge-Model. However, the fracture toughness value that has been predicted by finite element method from non –linear elastic analyses and from non –linear elastic-plastic analyses gives excellent results which are very close to the experimental results with error ratio ranging between (10% to 14%).

Study on Local Failure at Structural Discontinuities of Pressure Vessels

In the previous study of authors, the new fracture surface was proposed for ductile fracture and local failure considering the effects of hydrostatic stress. In this paper, the mechanism the dominant factors of local failure were studied in an elastic-plastic region. Experimental and analytical studies were made using circular plate specimens with a nozzle. The fracture test was performed in an elastic-plastic region at room temperature. Both ductile fracture and local failure were observed at structural discontinuities, according to the stiffness differences between attached nozzles and plates. In this study, the proposed fracture surface in an elastic-plastic region evaluated the fracture location accurately, for the both failure modes. It was concluded that the proposed fracture surface is applicable to predict the failure mode and the failure location of structural discontinuities.

Elastic–plastic characterization of microstructures through pull-in 4 point bending test

This paper presents a simple design of gold MEMS, with a central test specimen undergoing tensile loading, for the experimental characterization of elastic–plastic behavior using electrostatic actuation. A kinematic model for the test microstructures is presented that relates the experimentally measured deflection in the test specimen to the developed axial and bending stress. Moreover, an elastic–plastic beam bending model is presented to analyze the development of plastic hinges in the central test specimen. The design of test microstructures allows us to achieve stress values higher than the yield stress of the gold specimen before the pull-in effect, thus allowing to analyze the effect of elastic–plastic behavior on the static deflection profile of the central test specimen under repeated loading. The actuation voltage-deflection tests under repeated loading, both in the elastic and elastic–plastic region, allowed to estimate the applied stress limit for the onset of plasticity in gold thin film based MEMS devices.

Constitutive model and reinforcing mechanisms of uniaxial compressive property for reactive powder concrete with super-fine stainless wire

Super-fine stainless wire (SSW) is an excellent reinforcing filler for reactive powder concrete (RPC) due to its high mechanical property, favorable dispersibility, strong interface bonding with matrix, and micron diameter and high aspect ratio. In this paper, the uniaxial compressive strength, deformation and stress-strain curves of SSW reinforced RPC under different curing conditions are studied. Meanwhile, an uniaxial compressive constitutive model is established based on continuum damage theory and the reinforcing mechanisms are revealed through macroscopic, microscopic and Ca(OH)2 orientation analysis. The uniaxial compressive strength, elastic modulus and Poisson's ratio of RPC are increased by 85.3%, 58.2% and 114.8% respectively and the cyclo-hoop effect is weakened due to the addition of SSW. The ascending-stage of uniaxial compressive stress-strain curves of SSW reinforced RPC shows obvious elastic-plastic region and the longitudinal peak strain is enhanced by 73.8%. The established theoretical uniaxial compressive constitutive model can well describe the stress-strain relationship of SSW reinforced RPC. The change of damage variable demonstrates the delaying effect of SSW on cracks. The reinforcing mechanisms of SSW to RPC include interface effect, overlapping network effect, inter-anchor effect, bridging effect, torsion, stripping and snapping effect and decrease in crystal orientation index of Ca(OH)2.

Experimental Investigation of Compressed Thin-Walled Steel Members

The paper presents fundamental information about realized experimental-theoretical research to determinate the load-carrying capacities for thin-walled compressed steel members with quasi-homogenous and hybrid cross-sections. The webs of such members are stressed in the elastic-plastic region. This continuous research joins on previous research of the first author of the paper. The aim of this research is to investigate and analyse the elastic-plastic post-critical behaviour of thin web and its interaction with flanges. The experimental program, test members and their geometrical parameters and material properties are evident from table 1 and table 2 as well as from figure 1 and figure 2. The test arrangement and failures of the test members are illustrated on Figures 3, 4 and 5. Some partial results are presented in Table 3 of the paper, too.