Elasto-plastic Stress Research Articles

Experimental fatigue characterization and elasto-plastic finite element analysis of notched specimens made of direct-quenched ultra-high-strength steel

The low-cycle fatigue behavior of a direct-quenched ultra-high-strength steel was experimentally characterized and numerically modeled. Fatigue and cyclic parameters were obtained by conducting strain-controlled low-cycle fatigue tests on uniform-gage specimens. Surface residual stresses were minimized and axial deflection eliminated by optimization of machining parameters and post-machining electro-polishing. The steel material showed cyclic softening and decrease in yield strength. Cyclic softening, stabilized response, and the cyclic stress–strain curve were numerically simulated using finite element analysis with a model capable of describing nonlinear kinematic-isotropic hardening. The results showed good agreement with experimental values and validated the model’s ability to simulate the softening and cyclic stabilization of the material under investigation. The same numerical method was then used in elasto-plastic stress–strain analysis of notched specimens made of the same material to make fatigue life predictions. Estimated lives were compared with predictions made by analytical approximations such as the linear rule, Neuber’s rule, and the strain energy density method and verified by experimental data. Finite element analysis using stabilized cyclic response yields the most accurate predictions and, thus, provides an effective tool for the fatigue analysis of this material.

Incremental elastoplastic FEM for simulating the deformation process of suction caissons subjected to cyclic loads in soft clays

This paper presents an incremental elastoplastic finite element method (FEM) to simulate the undrained deformation process of suction caisson foundations subjected to cyclic loads in soft clays. The method is developed by encoding the total-stress-based bounding surface model proposed by the authors in the ABAQUS software package. According to the model characteristics, elastoplastic stress states associated with the incremental strains of each iteration are determined using the sub-incremental explicit Euler algorithm, and the state parameters describing the cyclic accumulative rates of strains are updated by setting state variables during the calculations. The radial fallback method is also proposed to modify the stress states outside the bounding surface to the surface during determination of the elastoplastic stress states. The stress reversals of soil elements are judged by the angle between the incremental deviatoric stress and the exterior normal vector at the image stress point on the bounding surface to update the mapping centre and state variables during cyclic loading. To assess the general validity of the method, the reduced scale model tests and centrifuge tests of suction caissons subjected to cyclic loads are simulated using the method. Predictions are in relative good agreement with test results. Compared with the limit equilibrium and quasi-static methods, the method can not only determine the cyclic bearing capacity, but can also analyse the deformation process and the failure mechanisms of suction caisson under cyclic loads in soft clays.

Effect of thermal gradients on stress/strain distributions in a thin circular symmetric plate

The analysis of thermally induced stresses in engineering structures is a very important and necessary task with respect to design and modeling of pressurized containers, heat exchangers, aircrafts segments, etc. to prevent them from failure and improve working conditions. So, the purpose of this study is to investigate elasto-plastic thermal stresses and deformations in a thin annular plate embedded into rigid container. To this end, analytical research devoted to mathematically and physically rigorous stress/strain analysis is performed. In order to evaluate the effect of logarithmic thermal gradients, commonly applied to structures which incorporate thin plate geometries, different thermal parameters such as temperature mismatch and varying constraint temperature were introduced into the model of elastic perfectly-plastic annular plate obeying the von Mises yield criterion with its associated flow rule. The results obtained may be used in sensitive to temperature differences aircraft structures where the thermal effects on equipment must be kept in mind.

Elasto-Plastic Stress Analysis in Rotating Disks and Pressure Vessels Made of Functionally Graded Materials

A new elastio-plastic stress solution in axisymmetric problems (rotating disk, cylindrical and spherical vessel) is presented. The rotating disk (cylindrical and spherical vessel) was made of a ceramic/metal functionally graded material, i.e. a particle-reinforced composite. It was assumed that the material's plastic deformation follows an isotropic strain-hardening rule based on the von-Mises yield criterion. The mechanical properties of the graded material were modeled by the modified rule of mixtures. By assuming small strains, Hencky's stress-strain relation was used to obtain the governing differential equations for the plastic region. A numerical method for solving those differential equations was then proposed that enabled the prediction of stress state within the structure. Selected finite element results were also presented to establish supporting evidence for the validation of the proposed approach.

Analysis of cavitation time effect on elastoplastic response of underwater rectangular plate subjected to impulsive loading

This paper focuses on the cavitation effect on nonlinear elastoplastic deformation rectangular aluminum plate subjected to underwater explosion loading. Cavitation is a phenomenon that may be occurred for plates in the process of underwater explosion forming. The total pressure of the explosion becomes zero at the cavitation time, so that the governing equations of motion will be different before and after the cavitation. As a result, in terms of analysis and design, the cavitation time is significant in studying the behavior of a rectangular plate at underwater explosive loading. Based on Hamilton principle and variation method the nonlinear equations of motion of an underwater rectangular plate subjected to explosive loading are obtained. Exact linear dynamic response of plate is derived by employing the eigen function and nonlinear dynamic response of plate is derived by employing the finite difference method (FDM). The linear and nonlinear work hardening material modeling is considered to define the elastoplastic stress–strain relations. Return mapping algorithm is applied to calculate the stress and strain in any steps of loading. Then, the displacement, velocity and generated stress of plate during cavitation time are calculated. Using von Mises yield criterion, one can distinguishes the cavitation with in elastic or plastic regimes. By recognizing the time of cavitation in the range of elastic or plastic, the displacement and velocity field of plate are determined in duration of explosive loading. Results show that the cavitation time is on the order of 5–10 μs. Depending on amount of charge mass and stand-off, the cavitation time may occur in elastic or plastic regime. The results obtained of linear exact solution considering the linear work hardening material modeling are compared to results obtained of FDM considering the linear and nonlinear work hardening material modeling.

Elastoplastic nominal stress effects in the estimation of the notch-tip behavior in tension

The evaluation of notch effects in low-cycle fatigue problems in general requires local plasticity calculations via the solution of a global Finite Element (FE) problem to obtain the cyclic elastoplastic (EP) stresses and strains at the notch tip, as well as the stress gradient effects around it. Moreover, this EP global FE approach needs to adopt an incremental plasticity formulation in every element of the studied piece that suffers plastic strains. Besides being not trivial to implement, these calculations are computationally intensive, especially when dealing with long loading histories, since they imply in having to solve the EP FE problem for the entire piece for every load increment of every load cycle. A much simpler approach is to perform a single linear elastic (LE) FE calculation on the entire piece for a static unit value of each applied loading, to find the stress and strain influence factors. The resulting LE values then require EP corrections to reproduce the true stresses and strains at the critical point of the component. Thus, an EP strain concentration rule must be assumed to estimate the actual notch-tip stresses and strains from the LE values. Perhaps the most used concentration rules are the ones proposed by Neuber and Glinka, which usually result in reasonable estimates in tension, especially under plane-stress conditions. However, most implementations of Neuber’s and Glinka’s rules assume the nominal stresses (which act away from the notch tip) are purely elastic, which can induce significant numeric errors even at stress levels much below the yield strength. In this work, Neuber’s and Glinka’s rules are presented in a formulation that assumes nominal stresses as EP instead of LE, highly improving the EP notch corrections, even under gross yielding of the net section. EP FE simulations on thin and thick specimens are used to verify the effectiveness of the proposed formulation, as well as to study 3D notch effects.

Elasto-Plastic Stress Analysis in a Ductile Adhesive & Aluminum Adherends

In this study, an elasto-plastic stress analysis is proposed in an aluminum adherend and a ductile adhesive. Elasto-plastic analysis was carried out for the aluminum adherend and DP460 ductile adhesive in a double-lap joint. The analytical solution was compared with the finite element solution. ANSYS 12 was used in the stress analysis. The analytical solution was performed for the one-dimensional case in the adhesive and the adherends. A FEM solution was given for the two-dimensional case. Similar results were obtained for both. In addition, the solution was carried out for brittle and ductile materials. The mechanical properties of the loctite were nearly the same as the ductile DP460 adhesive. It was observed that the ductile adhesive increased the strength of the structure due to the small shear stresses at the free ends of the adhesive.

Numerical validation of computational stress and strain analysis model for notched components subject to non-proportional loadings

In this paper, a previously developed computational model for the multiaxial stress–strain analysis of the notched bodies is further discussed and validated. The model calculates elastic–plastic stress–strain responses using linear elastic finite element solution of notched components. The validity of the model was presented by comparing results calculated from the proposed model against Finite Element Analysis (FEA) results of SAE 1070 steel notched bar subject to monotonic and cyclic non-proportional loading paths. The comparison showed that the model predicted notch-root elasto-plastic stresses and strains with good accuracy using linear-elastic stresses as a load input. The model becomes a significant advantageous tool and provides more efficient and simple analysis method in comparison to expensive experimental component tests and more complex and time consuming incremental non-linear FEA. The model is particularly efficient and practical to perform the elasto-plastic stress–strain analysis of notched components subjected to complex non-proportional loading paths.

Reliability analysis of static liquefaction of loose sand using the random finite element method

Purpose– Liquefaction of soils is defined as significant reduction in shear strength and stiffness due to increase in pore water pressure. This phenomenon can occur in static (monotonic) or dynamic loading patterns. However, in each pattern, the inherent variability of the soil parameters indicates that this problem is of a probabilistic nature rather than being deterministic. The purpose of this paper is to present a method, based on random finite element method, for reliability assessment of static liquefaction of saturated loose sand under monotonic loading.Design/methodology/approach– The random finite element analysis is used for reliability assessment of static liquefaction of saturated loose sand under monotonic loading. The soil behavior is modeled by an elasto-plastic effective stress constitutive model. Independent soil parameters including saturated unit weight, peak friction angle and initial plastic shear modulus are selected as stochastic parameters which are modeled using a truncated normal probability density function (pdf).Findings– The probability of liquefaction is assessed by pdf of modified pore pressure ratio at each depth. For this purpose pore pressure ratio is modified for monotonic loading of soil. It is shown that the saturated unit weight is the most effective parameter, within the selected stochastic parameters, influencing the static soil liquefaction.Originality/value– This research focuses on the reliability analysis of static liquefaction potential of sandy soils. Three independent soil parameters including saturated unit weight, peak friction angle and initial plastic shear modulus are considered as stochastic input parameters. A computer model, coded in MATLAB, is developed for the random finite element analysis. For modeling of the soil behavior, a specific elasto-plastic effective stress constitutive model (UBCSAND) was used.

An efficient approach to the analysis of rail surface irregularities accounting for dynamic train–track interaction and inelastic deformations

A two-dimensional computational model for assessment of rolling contact fatigue induced by discrete rail surface irregularities, especially in the context of so-called squats, is presented. Dynamic excitation in a wide frequency range is considered in computationally efficient time-domain simulations of high-frequency dynamic vehicle–track interaction accounting for transient non-Hertzian wheel–rail contact. Results from dynamic simulations are mapped onto a finite element model to resolve the cyclic, elastoplastic stress response in the rail. Ratcheting under multiple wheel passages is quantified. In addition, low cycle fatigue impact is quantified using the Jiang–Sehitoglu fatigue parameter. The functionality of the model is demonstrated by numerical examples.

Hyper-reduced predictions for lifetime assessment of elasto-plastic structures

Finite element (FE) elasto-plastic or elasto-viscoplastic simulations of complex components can still be prohibitive for lifetime predictions. There is a need for fast estimation methods of plasticity in a given region of interest, where a crack could be initiated. Some rules are already available for fast predictions of elasto-plastic stress and strain, by using elastic simulations. Furthermore, as shown by the Herbland’s model, inclusion theory can be incorporated in simplified rules to improve their accuracy. Recent advances in model reduction methods for nonlinear mechanical models give access to fast elasto-plastic or elasto-viscoplastic predictions having both accuracy and computational complexity in between usual FE predictions and these simplified rules. Hyper-reduction performs quite well in the simplification of elasto-plastic or elasto-viscoplastic models. Similarly to Herbland’s model, we show in this paper a first attempt to improve hyper-reduced models by the recourse to a virtual inclusion placed in the region of interest. In the proposed numerical example, a finite element model involving 5000 degrees of freedom is reduced to 12 variables. The mesh is also reduced to 550 elements over a total of 900 elements for the original mesh. The approximation error on the predicted plastic strains and stresses is lower than 3 % and the computational time is reduced up to a factor 5.

An improved rheology model for the description of the rate-dependent cyclic behavior of high damping rubber bearings

An improved rheology model, inspired from explicit experiments is conceived to represent rate-dependent cyclic shear behavior of high damping rubber bearings at subzero and room temperatures. Total stress has been decomposed into nonlinear rate independent elasto-plastic stress, nonlinear elastic stress and nonlinear visco-elasto-plastic overstress branches. To represent nonlinear viscosity behavior, ‘overstress branch’ has been generalized by putting linear elastic spring in parallel to nonlinear elasto-plastic model, placed in series with nonlinear dashpot. Constitutive relations for model elements have been designated for respective fundamental phenomenon observed in constant strain rate experiments. An optimum calculation approach is developed to determine a unique set of overstress parameters capable not only of representing constant strain rate cyclic tests but also sinusoidal tests with variable input strain rates. Essential abilities of the proposed model and adequacy of estimated parameters have been confirmed by comparing numerical simulation results with experiments conducted at −30°C, −10°C and 23°C.

Damage index for crack initiation of structural steel under cyclic loading

A damage index for crack initiation (DICI) with damage accumulation effects considered was introduced in this study. Cyclic tension and compression tests of notched bars were used to verify the proposed DICI. The local cyclic elasto-plastic stress–strain responses, used to calculate DICI, were analyzed using the incremental plasticity procedures of ABAQUS finite element code for various strain amplitudes. Two crack initiation criteria with DICI used, single point criterion and characteristic length criterion, were employed to investigate the crack initiation behavior of the specimens. The single point criterion for crack initiation is met when DICI exceeds 1 at any point of the continuum. The characteristic length criterion for crack initiation is met when DICI exceeds 1 over a critical length equal to the characteristic length. It was found that the single point criterion is applicable to fatigue crack initiation and ductile crack initiation separately, while the characteristic length criterion is feasible to simulate fatigue crack initiation and ductile crack initiation simultaneously.

Elastoplastic Analysis of Novel Parabola-Arc-Shaped Head for Internal Pressure Vessel

In this paper, the elastoplastic stress analysis of a novel parabola-arc-shaped head subjected to internal pressure has been carried out using finite element method. Limit loads and burst pressures are obtained for various geometric parameters and compared with the conventional torispherical and ellipsoidal heads. For the same middle diameter and thickness, the novel parabola-arc-shaped head shows better mechanical performance than the torispherical head. The burst pressure is mainly determined by the size of cylinder and the burst always occurs in cylinder. The head can improve the burst load when the cylinder is relatively short. The improvement of the novel parabola-arc-shaped head is almost the same as the ellipsoidal head, while the torispherical head is slightly inferior. As the novel parabola-arc-shaped head can be more easily formed with less material consumed compared to the conventional ones, it should thus be applicable in engineering practice.

Elastic-Plastic Constraints Analysis for Hole-Edge Crack

This paper mainly conducts an elastic-plastic constraint analysis on rectangular plate specimens with hole-edge crack under remote uniaxial uniformly distributed load by using J-A2 elastic-plastic fracture theory. In order to analyze the effect of orifice on elastoplastic stress field of hole-edge crack tip, this paper calculates a series of round hole-edge crack, diamond hole-edge crack and corresponding pure crack models. The interference effects of the orifice shape on elastic-plastic J integral and crack constraint parameter A2 are discussed. The results show that: the orifice has an amplification effect on the fracture driving force (J-integral), and this amplification effect in elastic-plastic is smaller than that in elastic; the orifice has a shielding effect on the crack tip constraint (A2 parameter), and this shielding effect gradually weaken with the crack increasing.

A 6-node co-rotational triangular elasto-plastic shell element

A 6-node co-rotational triangular elasto-plastic shell element is developed. The local coordinate system of the element is defined by the vectors directing from one vertex to the other two vertices and their cross product. Based on such a co-rotational framework, the element rigid-body rotations are excluded in calculating the local nodal variables from the global nodal variables. The two smallest components of each nodal orientation vector are defined as rotational variables, resulting in the desired additive property for all nodal variables in a nonlinear incremental solution procedure. Different from other existing co-rotational finite element formulations, both the element tangent stiffness matrices in the local and in the global coordinate systems are symmetric owing to the commutativity of the nodal variables in calculating the second derivatives of the strain energy with respect to the local nodal variables and, through chain differentiation, with respect to the global nodal variables. For elasto-plastic analysis, the Maxwell---Huber---Hencky---von Mises yield criterion is employed together with the backward-Euler return-mapping method for the evaluation of the elasto-plastic stress state, where a consistent tangent modulus matrix is employed. To overcome locking problems, the assumed linear membrane strains and shear strains are obtained by using the line integration method proposed by MacNeal, and the assumed higher-order membrane strains are obtained by enforcing the stationarity of the mixed displacement-strain canonical functional, these assumed strains are then employed to replace the corresponding conforming strains. The reliability and convergence of the present 6-node triangular shell element formulation are verified through two elastic plate patch tests as well as two elastic and five elasto-plastic plate/shell problems undergoing large displacements and large rotations.

Elastoplastic Analysis and Optimization Design for the Tube Channel End of Screw Lock Closure Type Heat Exchanger

With the usage of the FEM software ANSYS, an axisymmetric model for the tube channel end of a screw lock closure type heat exchanger was built. The elastic and elastoplastic stress analyses were carried out. The variations of the stress distribution at the root of threads and the contact pressure on threads engaged surfaces were invesgated. Furthemore, an optimization design based on the elastic model for this type heat exchanger was also conducted in order to obtain reasonable structure dimensions and make full use of materials.

Total-FETI domain decomposition method for solution of elasto-plastic problems

In this paper we present an algorithm for the parallel solution of the rate-independent elasto-plastic problems with kinematic hardening. We assume the von Mises plastic criterion and the associated plastic flow rule. The time discretization is based on the implicit Euler method. The corresponding one-time-step problem is formulated in the incremental form with respect to the unknown displacement and discretized spatially by the finite element method. We use an ‘external’ algorithm based on a linearization of the elasto-plastic stress–strain relation by the corresponding tangential operator and we parallelize the arising linearized problem by the Total-FETI method. The numerical experiments were carried out using our novel C/C++ library FLLOP (FETI Light Layer On top of PETSc) at HECToR supercomputer located at EPCC, UK.

Thermally-activated constitutive model including dislocation interactions, aging and recovery for strain path dependence of solid solution strengthened alloys: Application to AA5754-O

A thermally-activated constitutive model is developed based on dislocation interactions, crystallographic orientations and microstructural evolution to describe the elasto-plastic stress–strain behavior during multi-axial loading. The aim is to contribute to the quantification of complex strain path response in solid solution strengthened alloys. In detail, dislocation/dislocation interactions are incorporated in the model to quantify latent and kinematic hardening phenomena during loading path changes. Dislocation density-based constitutive relations are included to account for dislocation features such as dislocation forests, walls and channels. Moreover, dislocation/solute atom interactions are also considered in order to account for both dynamic and static strain aging as well as static recovery. The model is validated against multiple multi-axial data sets for AA5754-O with changes of loading path and various degrees of pre-strain and time intervals between tests.

Elasto-Plastic Stress Analysis of Thick Cylinders

– Pressure vessels often have a combination of high pressure together with high temperature such as gun barrels and high pressure hydraulic rams. For high pressure application, the cylindrical vessels are made to withstand the working pressure. These types of pressure vessels are made by two techniques, one is shrink-fit cylinders and other one is autofrettage cylinders. Autofrettage technique is used to ensure the pressure vessel highly strengthened due to prestressed effect causing the internal portion of the part to yield and resulting in internal compressive residual stresses. The present work is concerned about the elastoplastic stress analysis of thick cylinders. The numerical analysis is carried out on four different materials which are widely used in pressure vessels by using finite element software ANSYS. The elastic breakdown pressure, overstrain pressure, and bursting pressure of the cylinder are found out and the results are compared with experimental results.