Elastoplastic Stress Distribution Research Articles

Analytical and finite element investigation on residual stress analysis for composite thermoplastic cantilever beam under unique load

For a steel-fiber-based low-density homogenous composite thermoplastic cantilever beam, numerical (ANSYS APDL19) and analytical (MATLAB program) for elastoplastic stress distributions are achieved. At its free end, a thermoplastic cantilever structural member is loaded using a steady force. For orientation angles of (0°, 15°, 30°, 45°, 60°, 75° and 90°), the yield region's expansion and (σx)r are calculated. MATLAB program was used to determine the residual distribution of stress analytically. Both the yield zone that expands just at the top surface and the plastic zone that expands on both the top and bottom surfaces simultaneously are subjected to the elastic–plastic analysis. After the applied load has been freed, the components of residual distribution of stress are detected. Additionally, the distributions of the σx residual stress is established. By utilizing residual distribution of stress, the beam can be reinforced. The upper and lower edges of the beam are where the residual stress values are strongest. For the same load in the beam at orientation angles of (0°, 15°, 30°, 45°, 60°, 75° and 90°) the space amidst the free end and the plastically contracted region is determined. Lower discrepancy is evaluated for numerical (ANSYS APDL19) and analytical results.

Modeling of Stress Distribution and Fracture in ABS, PLA, and Alumina-Filled PLA Filaments and FDM-Printed Specimens

In the presented work, a probabilistic approach to fracture analysis of commercially available polyacrylonitrile butadiene styrene (ABS) and polylactide (PLA) filaments and fused deposition modeling (FDM)-printed tensile samples produced from them, as well as PLA filled with alumina (Al2O3) specimens, is discussed. The results of the analysis reveal the presence of symmetry between the stress distribution in the plastic–elastic and fracture stress regions. The value of the transition point from elastoplastic stress distribution to fracture distribution was established. It was shown that the probability density of the destruction of samples in a bound state obeys the Cauchy distribution. The resulting model well describes the stress distributions of tensile specimens, with a minimum deviation of 0.021% and a maximum deviation of 0.048% for the ceramic–polylactide (60Al2O3/40PLA) filament.

Fatigue crack growth modelling by means of the strain energy density-based Huffman model considering the residual stress effect

In this research work, the modelling of the fatigue crack growth behaviour of the 6061-T651 aluminium alloy through the Huffman fatigue crack growth approach, based on the strain energy density from dislocations and considering the residual stress effects was suggested. The Huffman fatigue crack growth model is based on the cyclic stress–strain behaviour of the material as well as the local elastoplastic stresses and strains obtained for a distance ahead of the crack tip (x), where those stresses are related to the fatigue damage of a crack increment Δa, as calibrator parameter. The calculations of the elastoplastic stresses and strains are done using Neuber’s or Glinka’s approach. Two approaches supported by the Noroozi and Huffman's suggestions to consider the residual stress effects were studied and discussed. Besides, in the modelling of the fatigue crack growth behaviour, the influence of the strain energy density calculated for values of critical dislocation density driven by the highest strain amplitude specimen and the mean value of the dislocation density for the available experimental fatigue results were also considered in this investigation. A comparison between the analytical solutions based on the Neuber and Glinka rules and numerical solutions from the finite element modelling of the CT geometry was done, where a satisfactory agreement for the elastoplastic stress distributions was found. The studied critical dislocation density values do not significantly influence the fatigue crack propagation behaviour. It is also concluded that the procedure for considering the residual stress effects influences the calibration parameter, Δa, being not possible to conclude which is the better method to describe the residual stress effects.

О ВОЗМОЖНОСТИ ОЦЕНКИ УСТОЙЧИВОСТИ ОТКОСОВ И СКЛОНОВ НА ОСНОВЕ РЕШЕНИЯ СМЕШАННОЙ ЗАДАЧИ ТЕОРИИ УПРУГОСТИ И ТЕОРИИ ПЛАСТИЧНОСТИ ГРУНТА

the article briefly describes the physical model of the mixed problem of the theory of elasticity and the theory of plasticity of the soil, identifies the features of its formulation and solution; formulas are presented for calculating stresses inside plastic regions and expressions that allow one to determine their position, dimensions and shape in the case of an elastoplastic stress distribution in a soil mass. A comparison is made of the results of experimental studies of the fracture processes of slope models from equivalent materials under loading, obtained independently by other authors, with the results of the analytical construction of plastic strain regions for the conditions of the mixed problem. It was established that the constructed areas are in satisfactory agreement with the results obtained in laboratory studies and with the results of field observations. The areas of plastic deformations for slope models of equivalent materials under breaking load are determined. The results of calculations of the stability of real natural slopes are presented, which include the calculation of stability margin coefficients and the construction of plastic regions for various values ​​of the lateral pressure coefficient of soils. Stability calculations are performed and their results are presented for real soil massifs

Elastoplastic Assessment of Limiting Internal Pressure in Thick-Walled Cylinders with Different Tension-Compressive Response

Elastoplastic calculation and stress distributions of limiting internal pressure in thick-walled cylinders are examined based on the twin-shear strength criterion. The calculations are especially versatile for quantitative evaluating the intermediate principal stress, different tensile-compression strength, and tension-compression modulus. The calculation results are verified by comparing with other data taken form the literature. Parametric studies were carried out to assess the influence of the strength parameter, radius ratio, tensile-compression strength ratio and tension-compression modulus. The proper choice of determining parameters is shown to be vital for the design of such components. It makes full use of the strength potentialities for thick-walled cylinders due to considering the intermediate principal stress. Limiting internal pressure variations with the radius ratio provide reference for selecting a reasonable wall thickness. The calculations have an important practical value for the optimum design and engineering application of thick-walled cylinders.

An improved three-point bending test method for the investigation of nanosecond laser dicing of ultrathin Si dies with Cu stabilization layer

The sidewall fracture strength of ultrathin Si dies with frontside and backside metallization layers cannot be determined directly from three-point bending (3PB) test. The complex 3PB elastoplastic stress distribution makes it difficult to determine the die sidewall fracture strength by analytical method or finite element analysis due to various theoretical and practical constraints. In this work, a selective chemical etching method has been developed for complete removal of the frontside and backside metallization layers on the ultrathin die without affecting the critical microstructure and strength of the die sidewall induced by laser dicing. By removing all the metallization layers on the die, the complex 3PB elastoplastic stress distribution is simplified to an elastic stress distribution. This enables a straightforward calculation of the die sidewall fracture strength using the standard 3PB tensile stress equation for a homogeneous linear elastic material with a rectangular cross section. Two chemical etchants were evaluated and found to be suitable but FeCl3 is preferred because of the much faster etching time. With this improved 3PB test method, the effect of nanosecond laser dicing on ultrathin Si dies with backside Cu layer was investigated. The die frontside and backside characteristic fracture strengths of ultrathin Si dies with varying backside Cu thickness were determined and correlated to TEM analyses of the compositions and microstructures at the fracture origins.

Strengthening and design of the linear hardening thick-walled cylinders using the new method of rotational autofrettage

The new approach introduced for the autofrettage called the rotational autofrettage is applied here for thick-walled cylinders made of materials with linear strain hardening behavior. The concept of the rotational autofrettage originates from the fact that large enough angular velocity in a thick-walled cylinder causes beneficial residual stress which is the prerequisite of the autofrettage process. For this purpose, elasto-plastic stress distribution in a rotating thick-walled cylinder are obtained analytically for both loading and unloading phases using Tresca's yield criterion and considering the bauschinger effect. In the following, the residual stress distribution are obtained to determine the best level of autofrettage for strengthening and design of thick-walled cylinder prior to industrial use with the aim of increasing strength-to-weight ratio. It is concluded that rotational autofrettage causes better results in comparison with the conventional method, pressure autofrettage. Moreover, rotational autofrettage method is used to obtain the best dimensionless thickness for a cylinder to withstand high internal pressure.

Elasto-plastic stress distributions in adhesively bonded double lap joints

Elasto-plastic stress analysis is an important solution for a used ductile adhesive in single or double lap solutions. After loading, the joint strength can be increased by residual stresses. In this study, an elasto-plastic stress analyses of the shear and peel stresses are carried out in a double-lap joint. The adhesive material is chosen as a ductile material which is DP460. Elasto-plastic solution of the shear stress is obtained in a simple and accurate form in one dimensional case. Then, the solution of the peel stress is performed by considering the shear stress in the elasto-plastic form. In this solution, the boundary conditions are satisfied by the Newton–Raphson method. A good agreement is obtained between these analytical and numerical (ANSYS 10) solutions. The values are calculated highest at the ends of the adhesive.

Exact Solutions for Elastoplastic Stress Distribution in Functionally Graded Curved Beams Subjected to Pure Bending

The material of the beam is presumed to be isotropic and ideally elastic-plastic and the elastic modulus and yield limit vary radially according to power law functions. Based on Tresca's yield criterion and its associated flow rule, the expressions of the stresses and displacements in four different stress states are presented. The condition to achieve the concurrent yielding on the inner and outer surfaces is given explicitly. The position of the neutral plane and the plastic limit bending moment in a completely plastic state are determined. The distinct characteristics of elastoplastic behavior of functionally graded materials (FGMs) curved beam are shown in examples.

Analysis on Elastoplastic Stress Distribution in a Layered Cylindrical Vessel With Interlayer Gaps

In this paper, the formulae for elastoplastic stress distribution in layered cylindrical vessel layers with gaps have been provided. These formulae are based on the modified Pimshtein formulae for the elastic stress of layers. Plane strain with ideal elastoplastic model of materials is adopted. A practice example is presented to show how the formulae can be used for elastoplastic stress calculation. The hoop, radial, axial, and Von Mises equivalent stresses are obtained. The calculation result showed that the stress state of layered cylindrical vessel is more complex than that of monobloc cylindrical shell due to the interlayer gaps. The stress distribution is discontinuous. Calculation results obtained theoretically were compared to those obtained by finite element method (FEM). It shows that the results from the proposed formulae are in good agreement with finite element results.

Advanced Finite Element Modelling of Composite Beams with High Strength Materials and Deformable Shear Connectors

This paper presents a comprehensive numerical investigation into the structural behaviour of simply supported composite beams with high strength materials and deformable shear connectors. Advanced two and three dimensional finite element models of the simply supported composite beams are established, and they have been carefully calibrated against the results of two test beams reported in the literature. The two dimensional finite element models are then extended to investigate the structural behaviour of simply supported composite beams with different combinations of high strength steels and concrete. A number of key findings of the numerical investigation are presented after careful consideration on the predicted moment capacities of the composite beams determined from various methods. It is shown that an elasto-plastic stress distribution should be adopted to determine the moment capacities of composite beams using a wide range of steel and concrete materials with high structural adequacy.

205102 レール鋼における非比例混合モードI+II負荷における疲労き裂成長方向(OS04 材料・機械・構造物における強度と寿命2,オーガナイズド・セッション)

Two criteria for the prediction of incipient crack path direction of non-proportional mixed mode I+II loading in rail steel are investigated. The analysis is based on 2D plane strain FE-simulations in which actual elasto-plastic stress distribution is used for the maximum tangential stress (MTS) criterion and maximum tangential stress range (MTSR) criterion. The purpose of the analysis is to compare the numerical results with experimental results. It is shown that both the MTS and MTSR criteria including plasticity and sophisticated work hardening law are well suited to predict incipient crack growth directions for the rail steel under non-proportional loading.

Elasto-Plastic Stress Distribution in Triplate Joint Assembly under Bending Moment

Pre-produced triplate transition joint assemblies are widely used in shipbuilding industry to make welds between aluminum and steel for a number of years now. The straight-shaped transition joint assemblies are bent during shipbuilding. So it is necessary to study the residual stresses created by punch forming, which would have heavy effects on the quality of structural parts. ABAQUS is a suite of powerful engineering simulation programs, based on the finite element method. In this paper, ABAQUS was used as the main tool to simulate the residual stresses in a triplate transition joint after unloading. Punch-pressing was carried to simulate bending moment in ABAQUS. The triplate is consisted of baselayer (steel: Lloyd’s Shipplate Gr. A), interlayer (pure aluminum: Al99.5) and superlayer (Al-Mg alloy: AlMg4.5Mn). Results from the ABAQUS analysis showed that increasing the radius of punch significantly reduced the von Mises residual stresses in steel. Changes of von Mises residual stresses in interlayer (Al99.5) and superlayer (AlMg4.5Mn) were negligible.

Estimation of Elastoplastic Thermal and Residual Stresses in a Thermoplastic Composite Disc Under Uniform Temperature Effect

In this study, an elastoplastic thermal stress analysis has been carried out on a thermoplastic composite disc that is unidirectionally reinforced by steel fibers. The finite element method (FEM) was used to compute thermal elastic and elastoplastic stress distributions in the model of the composite disc. The solution is performed using the ANSYS program. In order to evaluate the effects of uniform temperature, different temperature loadings are applied to the disc model uniformly. Both radial and tangential stresses are calculated under a uniform temperature loading which is chosen from between 80 to 120 C. Due to the composite disc having different thermal expansions in radial and tangential directions, thermal stresses were calculated by applying uniform temperature loading. The magnitude of tangential stress components for both elastic and elastoplastic solutions is higher than that of radial stress components. Moreover, residual stress components are obtained using the results of elastic and elastoplastic solutions. The calculated results point out that distributions and values of improved thermal stresses and residual stresses are considerably influenced with increasing uniform temperature loading.

1215 堀・亀田の応力逆解析法による弾塑性応力分布の推定(OS-12D 材料の組織・強度に関するマルチスケールアナリシス(微視的変形組織のキャラクタリゼーション),OS-12 材料の組織・強度に関するマルチスケールアナリシス)

The present study has applied Hori and Kameda's stress inversion method to the estimation of elasto-plastic stress distributions in Al-Mg polycrystalline materials. The method can estimate 2D elasto-plastic stress distributions from deformation distributions measured in a structure by using only the elastic moduli of the material of the structure. First, computer codes have been developed based on the present stress inversion method. Then, elasto-plastic 2D FEM analyses of stress concentration problems caused by elliptic holes and rectangular inclusions were made. Comparison of the results obtained by the FEM analyses and the stress inversion method showed that the stress inversion method can estimate elastic and elasto-plastic stress distributions from deformation/strain distributions with reasonable accuracy. Finally, the elasto-plastic stress distributions in Al-Mg were estimated by using deformation distributions measured by the digital image correlation method and it was found that stress concentration occurred near triple junctions of grain boundaries.

Numerical simulation of springback using enhanced assumed strain elements

The quality of springback prediction for a sheet metal forming process depends on a precise estimate of the elasto-plastic stress distribution throughout the metal sheet. The use of low-order conventional finite elements may be, without any proper treatment, responsible for low quality prediction because of volumetric and shear lockings. In this study, the enhanced assumed strain technique will be exploited for locking removal. The quality of the numerical simulation is evaluated through a comparison with other popular techniques like selective and uniform reduced integration. In contrast to the latter, and thanks to a full numerical integration scheme, the enhanced assumed strain element is very efficient in accurately capturing the development of plastic flow. This enables a reliable prediction of springback even with a rather coarse mesh.

破壊力学 弾塑性境界要素法による異種接合材界面端の解析

Elastoplastic boundary element analysis is carried out to investigate the effect of linear hardening coefficient on the stress singularity and stress field near an interface edge in bonded dissimilar materials. The results show that the elastoplastic stress distribution near an interface edge can be divided into 3 regions, i.e., elastoplastic singular stress dominated zone, transition zone and elastic zone, sizes and properties of which depend on the size of yielding zone and the hardening coefficient. If the linear hardening coefficient is relatively large, the elastoplastic stress distribution agrees with the quasi-elastic theoretical result. It is also found that the transition zone increases and the elastoplastic singular stress dominated zone decreases with decreasing the hardening coefficient. If the linear hardening coefficient is small enough, the transition zone may become the main part of the yield zone, and the theoretical results may be correct only in a very small region near the edge, hence it would lose physical meanings for the evaluation of elastoplastic fracture. On the other hand, for small scale yield problems, the numerical results show that the behavior of stress distribution in the elastic zone is almost similar to the elastic theoretical results (i.e. the stress singularity order is almost the same), but the stress intensity coefficient becomes somewhat larger.

A Simplified Method for Estimating the Elastoplastic Stress and Strain Distribution on 60.DEG. V Notch Section.

A simplified method for estimating the elastoplastic stress and strain distribution on 60°V notch section from a result of elastic analysis was presented. Elastic and elastoplastic analyses of 60°V notched bars and plates subjected to tensile force were carried out by FEM. It was found from these analyses that the distributions on notch section of equivalent strains obtained from equivalent stresses, stress ratios and strain ratios in elastic condition were analogous to those distributions in elastoplastic condition. The proposed simplified method was based on these analogies, the total strain theory and equilibrium condition of axial force. Good estimated results of the stress and strain distribution, the maximum notch strain and the plastic zone size were obtained. The maximum notch strain estimated by the simplified method was also compared with that by Neuber's and Glinka's methods.

Stress concentration factors within bolt-nut connectors under elasto-plastic deformation

The elasto-plastic stress distributions within straight and tapered bolt-nut connectors are studied in this paper by using the virtual contact loading method. Based on a simplified axisymmetrical model, the virtual contact loads are used to simulate the elasto-plastic contact phenomena between the mating screw flanks and the detailed stress and load distributions along the threads have been found. The calculated results show that dangerous stress occurs at the thread roots and the first pair of thread roots are the first to undergo the plastic deformation.

Elastoplastic Finite Element Analysis and Strength Evaluation of Adhesive Butt Joints of Similar and Dissimilar Hollow Shafts Subjected to External Bending Moments

Stress distributions and deformation of adhesive butt joints are analyzed by an elastoplastic finite element method when the joints of similar and dissimilar shafts are subjected to external bending moments. The effects of the ratio of Young's modulus for the adherends to that for an adhesive and the effects of the adhesive thickness on the interface stress distribution are investigated. Joint strength is predicted by using the elastoplastic interface stress distributions. It is found that the singular stress at the edge of the interfaces increases with an increase of the ratio of Young's modulus. Measurement of strains in joints and experiments on joint strength were conducted. The numerical results are in fairly good agreement with the experimental results. It is observed that the joint strength for dissimilar shafts are smaller than those for similar shafts. A fracture of dissimilar adhesive up-bonded shafts occurred from the interface of the adherend with smaller Young's modulus. It is seen that joint strength increases as the adhesive thickness increases.