Elastic-plastic Material Behavior Research Articles

Extension of the Freiberg Layer Model by Means of Elastic–Plastic Material Behavior

Finite element method simulations offer deep and detailed modeling of complex processes, but with high effort of computation power and time. For the special purpose of flat rolling, a layer model was developed by Schmidtchen before based on the classic elementary theory of plasticity with the purpose to model inhomogeneous behavior with significant lower effort at computation. This model considered the layers only as rigid or in plastic deformation state. Herein, the model is extended by elastic material behavior to get closer to the depth of finite elements method (FEM) models. The results are first compared with a FEM simulation and measurements from the literature. The current model is found to fit well the FEM results as well as the measurements. Second, the results are compared with classic elementary theory and the layer model of Schmidtchen. From these comparisons is found, that the main elastic influences on the stress curve shape are due to the full elastic zones. Elastic deformations in the plastic regions are found to be smaller, but growing on transition from block rolling to thin sheet rolling.

Effect of autofrettage on the ultimate behavior of thick cylindrical pressure vessels

Major applications of thick cylinders are in the defense sector. Stress distributions especially under elastic-plastic conditions are more complex in thick cylinders. Though the cylinder may not be strained to ultimate in service, assessment of factor of safety is essential. Simulating elastic-plastic material behavior of cylinders using the uni-axial test data is more dependable and the finite element analysis (FEA) software has got this capability. A procedure using a suitable material model is demonstrated in this study utilizing the FEA software Ansys. The instability criterion followed in Svensson's pressure expansion relationship is used in the process of FEA. The predicted failure pressure is very close to the literature test data as well as few theories that have been highlighted. Moreover, thick cylinders are mostly subjected to autofrettage in applications like gun barrels to enhance service pressure and fatigue life. Hence it is attempted to simulate the development of residual stress due to autofrettage and its effect on the ultimate behavior on the pressure vessels. The residual stress developed is superimposed on the stresses due to internal pressure which causes the redistribution of stresses throughout the thickness. There is a marginal increase in burst pressure due to autofrettage. Though the effect could be made significant by increasing the autofrettage pressure, it gives detrimental effects on the other side by developing tensile residual stresses on the external surface. Hence, with the permissible extent of autofrettage, the effects are found to be marginal and this knowledge helps assess the safe loading limits.

Correlations between crack initiation and crack propagation lives of notched specimens under constant and variable amplitude loading

AbstractThis paper starts with an overview of the application of the three guidelines (GL) of the German Research Association of Mechanical Engineers (FKM). Each of these provides algorithms for calculating fatigue lives of components under constant or variable amplitude loading, however, with underlying different failure criteria, that is, technical crack initiation life (GL‐nonlinear), fatigue crack growth life (GL‐fracture mechanics), and total fracture life (GL‐linear). Since the GL‐linear only considers linear‐elastic material behavior in the fracture fatigue life calculation, the guideline is not capable for the LCF and is not able to take sequence effects into account. For a better approximation of fracture fatigue lives, the elastic–plastic material behavior has to be taken into account. This paper introduces the U‐Concept which has been evaluated from a large structural durability database from the literature with more than 1,500 experiments for constant and more than 700 experiments for variable amplitude loading. The U‐Concept is a small add‐on to the local strain approach (LSA) which is the backbone of the GL‐nonlinear. It enables (1) to directly calculate the fatigue life to total fracture based on elastic–plastic material behavior according to the LSA or (2) to estimate the remaining fatigue life from crack initiation to fracture without a crack growth simulation. Furthermore, the U‐Concept needs no experimental determined crack growth parameters, the only necessary material parameter is the ultimate tensile strength Rm. The U‐Concept is therefore easy applicable for industrial users and increases the accuracy of the approximated fatigue lives by considering the elastic–plastic material behavior.

Design Synthesis Through a Markov Decision Process and Reinforcement Learning Framework

AbstractThis article presents a framework that mathematically models optimal design synthesis as a Markov Decision Process (MDP) that is solved with reinforcement learning. In this context, the states correspond to specific design configurations, the actions correspond to the available alterations modeled after generative design grammars, and the immediate rewards are constructed to be related to the improvement in the altered configuration’s performance with respect to the design objective. Since in the context of optimal design synthesis the immediate rewards are in general not known at the onset of the process, reinforcement learning is employed to efficiently solve the MDP. The goal of the reinforcement learning agent is to maximize the cumulative rewards and hence synthesize the best performing or optimal design. The framework is demonstrated for the optimization of planar trusses with binary cross-sectional areas, and its utility is investigated with four numerical examples, each with a unique combination of domain, constraint, and external force(s) considering both linear-elastic and elastic-plastic material behaviors. The design solutions obtained with the framework are also compared with other methods in order to demonstrate its efficiency and accuracy.

Round robin analysis to investigate sensitivity of analysis results to finite element elastic-plastic analysis variables for nuclear safety class 1 components under severe seismic load

As a part of round robin analysis to develop a finite element elastic-plastic seismic analysis procedure for nuclear safety class 1 components, a series of parametric analyses was carried out on the simulated pressurizer surge line system model to investigate sensitivity of the analysis results to finite element analysis variables. The analysis on the surge line system model considered dynamic effect due to the seismic load corresponding to PGA 0.6 g and elastic-plastic material behavior based on the Chaboche combined hardening model. From the parametric analysis results, it was found that strains such as accumulated equivalent plastic strain and equivalent plastic strain are more sensitive to the analysis variables than von Mises effect stress. The parametric analysis results also identified that finite element density and ovalization option in the elbow elements have more significant effect on the analysis results than the other variables.

Estimation of elastic–plastic notch strains and stresses using artificial neural networks

AbstractThe prediction of fatigue lives of metallic components using the notch strain approach is based on local stresses and strains. These can be determined either by analytical approximation formulas such as Neuber's rule based on linear elastic stresses or by finite element analysis with elastic–plastic material behavior. The latter has the disadvantage of longer computation times.This paper discusses a draft for application of artificial neural networks as an alternative approach for estimating uniaxial and multiaxial proportional elastic–plastic stresses and strains in notch roots based on linear elastic stresses. These networks are trained on results from elastic–plastic finite element analyses on flat bars notched on both sides and circumferentially notched shafts to predict local stresses. The resulting accuracy is compared to the analytical approximation formulas.The research findings confirm that neural networks can estimate local stresses with similar scatter and better mean value compared to analytical formulas.

Elastic-plastic analysis of reinforced concrete frame buildings: Developing a new software package

In this work we will explain a new methodology that have been utilized in a new software package (program) to determine the lateral loads at which a 3D reinforced concrete frame building collapses. The solution is represented by forming the capacity curve (force–displacement) of the structure taking into account the elastic-plastic behavior of the element materials represented by plastic hinges positioned at the ends of the linear elements. This work takes into account only the plastic hinges caused by bending moments. The program is based on finite elements method and capable of analyzing and designing three dimensions buildings. The program provides a drawing environment (3D view, plan view, elevation view) with tools to create the model and to perform the structural analysis and design.

Optimum Design of Reinforced Cylindrical Shells Under Combined Axial Compression and Internal Pressure

This paper discusses the use of the random search method for the optimal design of single-layered rib-reinforced cylindrical shells under combined axial compression and internal pressure with account taken of the elastic-plastic material behavior. The optimality criterion is the minimum shell volume. The search area for the optimal solution in the space of the parameters being optimized is limited by the strength and stability conditions of the shell. When assessing stability, the discrete rib arrangement is taken into account. In addition to the strength and stability conditions of the shell, the feasible space is subjected to the imposition of constraints on the geometric dimensions of the structural elements being optimized. The difficulty in formulating a mathematical programming problem is that the critical stresses arising in optimally-compressed rib-reinforced cylindrical shells are a function of not only the skin and reinforcement parameters, but also the number of half-waves in the circumferential and meridional directions that are formed due to buckling. In turn, the number of these half-waves depends on the variable shell parameters. Consequently, the search area becomes non-stationary, and when formulating a mathematical programming problem, it is necessary to provide for the need to minimize the critical stress function with respect to the integer wave formation parameters at each search procedure step. In this regard, a method is proposed for solving the problem of optimally designing rib-reinforced shells, using a random search algorithm whose learning is carried out not only depending on the objective function increment, but also on the increment of critical stresses at each extremum search step. The aim of this paper is to demonstrate a technique for optimizing this kind of shells, in which a special search-system learning algorithm is used, which consists in the fact that two problems of mathematical programming are simultaneously solved: that of minimizing the weight objective function and that of minimizing the critical stresses of shell buckling. The proposed technique is illustrated with a numerical example.

An Efficient Multi-Scale Modeling Method that Reveals Coupled Effects Between Surface Roughness and Roll-Stack Deformation in Cold Sheet Rolling

Abstract In thin-gauge cold rolling of metal sheet, the surface roughness of work rolls (WRs) is known to affect the rolled sheet surface morphology, the required rolling load, and the roll wear. While modeling of rough surfaces using statistical asperity theory has been widely applied to problems involving semi-infinite solids, the application of asperity distributions and their elastic-plastic behavior has not been considered in roll-stack models for cold sheet rolling. In this work, a simplified-mixed finite element method (SM-FEM) is combined with statistical elastic-plastic asperity theory to study contact interference and coupling effects between a rough work roll (WR) surface and the roll-stack mechanics in cold sheet rolling. By mixing equivalent rough surface contact foundations, Hertz foundations, and Timoshenko beam stiffness, an approach is created to efficiently model interactions between the micro-scale asperities and the macro-scale roll-stack deformation. Nonlinearities from elastic-plastic material behavior of the asperities and the sheet, as well as changing contact conditions along the roll length, are also accommodated. Performance of the multi-scale SM-FEM approach is made by comparison with a continuum finite element virtual material model. 3D studies for a 4-high mill reveal new multi-scale coupling behaviors, including nonuniform roughness transfer, and perturbations to the sheet thickness “crown” and contact force profiles. The described multi-scale SM-FEM approach is general and applies to rough surface contact problems involving plates and shear-deformable beams having multiple contact interfaces and arbitrary surface profiles.

Experimental 3D characterization and parametrization of an anisotropic constitutive law for a synthetic nonwoven

The usage of synthetic nonwoven materials is gaining importance in filtration. However, the complex material behavior of these synthetic, fiber-based materials is challenging for the manufacturing departments. The materials are exhibiting a highly anisotropic elastic-plastic material behavior. A material testing program was conducted to characterize the unknown characteristic material behavior of synthetic nonwoven filter media in all three spatial directions for the load cases of tension, compression, and shear for the first time. For conversion processes like cutting, embossing, calendering, and pleating, the out-of-plane properties are essential for the accurate description of the material behavior. Using an ARCAN device, it is possible to do the necessary tests to determine the out-of-plane properties. The test results were used to calibrate a suited anisotropic material model for fibrous and porous materials. Parallels and differences in the characteristic material behavior between cellulose and synthetic nonwoven filter media are discussed.

Plastic Limit Analysis Using the Simplified Theory of Plastic Zones

Abstract The simplified theory of plastic zones (STPZ) was mainly developed to determine strain ranges and accumulated strains in the state of shakedown at cyclic loading between prescribed levels of loading. Kinematic hardening is an indispensable feature of the STPZ. The plastic limit load, however, is defined for monotonic loading and elastic–plastic material behavior without hardening. Simply assigning a zero value or a numerically very low value of the tangent modulus when applying the STPZ is generally not possible due to arising numerical instabilities. It is, therefore, not immediately obvious how the STPZ can be used to determine the maximum load level that can be applied to a structure without developing a kinematic mechanism. This paper describes the theory and the analysis steps required and provides some illustrative examples. Typically, between one and three linear elastic analyses and some local calculations are required to provide either the exact value or at least a reasonable estimate of a range of the plastic limit load, as well as of the associated stress and strain fields and displacements that are not provided by classical limit analysis.

Assessment of service loads and material influence on the lifetime of thick-walled nodular cast iron components

To reduce weight and increase power as well as utilisation of nodular cast iron components, e.g. for wind turbines and heavy industry parts, locally higher strength need to be withstood by the material. This becomes crucial when additional overloads, coming from a storm, a grid loss during operation or a misuse, influence the structure of thick-walled components, causing high local elastic-plastic deformations. In this case, the cyclic, elastic-plastic material behaviour and its development under cyclic loading are important and have to be considered during component design.To assess the material’s local elastic-plastic material behaviour under the influence of overloads, strain-controlled fatigue tests, under constant and variable amplitude loading, were performed under alternating loading, R = −1, with unnotched specimens removed from cast blocks, a main frame and two planet carriers of wind turbines made from EN-GJS-400-18U-LT, EN-GJS-700-2, ADI-800 and ADI-900.By using two different load-time histories with a bulky and a more linear form, derived from local hot spots at a wind turbine’s hub and a main frame, in a first step, the lightweighting potential could be determined by comparing the S-N curves for constant and variable amplitude loading. In order to analyse the influence of an additional overload during usage, in additional test series, a maximum compressive overload of 0.5 and 1.0% total strain under tensile loading was included in the load sequence and the results compared with those without an overload.

Identification of combined hardening model parameters by considering pre-tensile stress for 2024-T3 aluminum alloy

The nonlinear hardening of the initial cycle is quite different from subsequent cycles under cyclic loading because of pre-tensile stress in work hardening metal materials. This paper investigates parameters of nonlinear combined hardening model by considering the effect of pre-tensile stress. The parameters of combined hardening model were fitted by three kinds of cyclic loading test data of 2024-T3 aluminum alloy. The finite element simulation with initial conditions representing the pre-tensile stress and experiment were analyzed to illustrate availability of calibration method of hardening parameters. The ratchet effect of asymmetric cyclic loading was predicted. The results show that compared with the curve without initial conditions, the changing trend of simulated stress-strain cyclic curves with initial conditions is more consistent with that of the test curve. The effect by adding initial condition elastic-plastic mechanical behavior in stress controlled loading becomes more pronounced than strain controlled loading. Under different loading modes, the metal materials exhibit cyclic hardening, average stress relaxation, ratchet effect and other cyclic effects. These results are of great significance for understanding the elastic-plastic deformation behavior of metal materials.

Numerical study of elastic-plastic behaviour of pore-containing materials: effects of pore arrangement

Numerical study of elastic-plastic behaviour of pore-containing materials: effects of pore arrangement

Numerical study of elastic-plastic behaviour of pore-containing materials: effects of pore arrangement

Numerical study of elastic-plastic behaviour of pore-containing materials: effects of pore arrangement

Compression zone with partial stiffeners in beam-to-column steel connections

The compression zone in beam-to-column connection can generally imply the use of transverse stiffeners. This paper presents the results of experimental tests to evaluate the strength of steel panels with various transverse stiffener configurations under concentrated load. These results are used to validate the developed finite element models. Twelve panels made of either hot rolled I-sections or welded I-sections have been tested. Different transverse stiffeners are studied including single sided, double sided and partial stiffeners. The main observed results are the maximum strength and the failure mode. The results of the experimental tests are compared with those given by the finite element model using shell elements. The comparison makes it possible to calibrate the nonlinear model considering the elastic-plastic behavior of materials and large displacements. Furthermore, the results are compared with existing analytical formulas for unstiffened and fully stiffened panels to evaluate their accuracy.

Integral treatment of butt joints for the fatigue life assessment in the low cycle fatigue regime

The framework for a fatigue assessment of welded joints under service loading conditions of crane structures from the low cycle to the high cycle fatigue regime includes the consideration of elastic-plastic material behavior, variable amplitude loading, and acceptable calculation times. Therefore, an integral treatment of butt joints has been developed for fatigue life estimation. The butt weld is considered in its entirety, so that it can be described by its cyclic behavior. The evaluation of the cyclic stress-strain behavior and tri-linear strain-life curves of butt joints for different high-strength, fine-grained structural steels, derived by strain-controlled fatigue tests, is the basis for this description. This procedure is not limited to conventionally applied gas metal arc welding only, but also the fatigue assessment of laser beam welding is possible, for example. Cyclic transient effects have been analyzed and a distinctive cyclic softening is described by linearization of Ramberg-Osgood parameters, depending on the damage content of each cycle derived from constant amplitude, strain-controlled tests. On the basis of the cyclic behavior in combination with memory and Masing behavior, a simulation of the stress-strain paths of investigated butt welds, under constant and variable amplitude loading, has been performed. Damage parameters are used to accumulate the damage cycle by cycle in order to derive the fatigue lifetime. Finally, calculated fatigue lives were compared with experimentally determined lives, showing the impact of this procedure.

Is the assumption of linear elasticity within prosthodontics valid for polymers? -An exemplary study of possible problems.

As shown in previous studies within other scientific fields, the material behavior of polymethyl methacrylate (PMMA) is viscoelastic-viscoplastic. However, in dental biomaterial science it is mostly considered as linear elastic or elastic-plastic. The aim of the present study was to evaluate, whether the assumption of elastic or elastic-plastic material behavior for PMMA is a practicable simplification or a potential source of error, especially considering clinical loading conditions. Telio-CAD was tested in three-point bending tests with different test velocities to examine the material behavior at different initial loading rates. Additionally, a dynamic-mechanical-thermal-analysis at different frequencies and temperatures was used. Here, a significant influence of loading rate and temperature as well as stress relaxation and creep were observed. To describe the rate-dependency of the elastic modulus, a new model was created, from which the elastic modulus can be calculated with a given strain rate. This model was validated using linear elastic finite element analysis.

Prediction of elastic-plastic deformation of nanoporous metals by FEM beam modeling: A bottom-up approach from ligaments to real microstructures

For the prediction of elastic-plastic deformation behavior of nanoporous materials, a computationally efficient method is needed that integrates the complex 3D network structure and the large variation of ligament shapes in a representative volume element. Finite element simulations based on beam elements are most efficient, but for a quantitative prediction, a correction is required that accounts for the effects of the mass around the junctions. To this end, a nodal correction is presented that covers a wide range of parabolic-spherical ligament shapes. Smooth functions are provided that define the extension of the nodal corrected elements along the ligament axis, their radius and their yield stress as functions of the individual ligament shape. It is shown that the increase in radius of the nodal beam elements can be replaced by scaled material parameters. Simulations of randomized FEM beam networks revealed that, in relation to the randomization of the ligament axis, the distribution of the ligament shape has a stronger impact on the macroscopic stress–strain response and should thus receive particular attention during the characterization of nanoporous microstructures. This also emphasizes the importance of the thickness analysis via image processing. Combining a nodal corrected FEM beam model with geometry data derived from image multiplication of the skeleton and Euclidean distance transform of a nanoporous gold FIB-SEM tomography dataset significantly improves the prediction of the stress–strain curve. The remaining deviation is expected to stem from the known underestimation of the real ligament diameter by the Euclidean distance transform as well as local variations in the circularity of the ligaments.

A damage constitutive model and its characterization parameters identification for elastic-plastic materials

This paper proposes a simple damage constitutive model for elastic-plastic materials on the basis of the classical elastic-plastic constitutive model and damage mechanics theory. Based on the simple damage constitutive model, ABAQUS built-in Python software was used to develop the virtual experimental platform, and the whole process simulation of the specimens stretching until the fracture was carried out. The correspondence between the damage characterization parameters and the performance indexes such as the fracture strain and the percentage reduction of area was studied. According to the comparison of the virtual/real test results of ZL114A, the situation shows that the simple damage constitutive model can realize the high fidelity simulation of the damage behavior of elastic-plastic materials. The relative accuracy of the important material property parameters such as the ultimate strength, the percentage total elongation at fracture and the percentage reduction of area reaches 5%.