In this paper, we investigate the computational efficiency of explicit and implicit integration schemes for hyperelastic-plastic combined hardening plasticity and examine the influence on the simulated springback in sheet metal forming. Due to the deviatoric character of the evolution equations, the finite strain combined hardening model discussed here is integrated by means of the exponential map algorithm in order to fulfil plastic incompressibility. We focus here on different possibilities of evaluating the exponential tensor functions of the material model. One option is to use the spectral decomposition to evaluate the exponential tensor functions in closed form. Alternatively, the latter functions can be evaluated by Taylor series expansion. Furthermore, we examine the potential of an explicit formulation of elasto-plasticity with combined hardening regarding accuracy and efficiency. The material model equations have been implemented as user material subroutines UMAT and VUMAT for use in the commercial solvers ABAQUS/Standard and ABAQUS/Explicit, respectively. The numerical models are applied to the finite element simulation of draw bending, where the forming step is simulated both in implicit and explicit manner, whereas the ensuing springback step is carried out only implicitly.

The roller profile appears to be the key element to attain a longer rating life for both cylindrical and tapered roller bearings. A genuine elastic analysis is able to optimize the roller profile to obtain a stress distribution in the contact zones that provides enhanced operational reliability and greater insensitivity to misalignment. For traditional cylindrical-crowned roller profile design class I discontinuities exist at the intersection points of roller profile with the crowning radius as well as at the end chamfer. In an elastic analysis these discontinuities generate very sharp increases in pressure distribution diminishing the rating life of the bearing. In fact, these local increases in pressure distribution are able to overcome, locally, the yield limit and to induce both plastic deformations and residual stresses. After a certain number of cycles the material will shakedown elastically to a slightly modified roller profile and a stable state of compressive residual stresses. If were taken place, these changes have to be considered in the life evaluation. An analysis model has been developed to simulate the nonlinear strain rate dependent deformation of rolling bearing steel stressed in the elastic-plastic domain. The model is developed in the frame of the incremental theory of plasticity by using the von Mises yield criterion and Prandtl-Reuss equations. By considering an isotropic and non-linear kinematic hardening laws the model accounts for the cyclic hardening phenomena. For each new load increment new increments for the components of stress and strain tensors, but also increments of residual stresses, are computed for each point of the 3D mesh. Both the new contact geometry and residual stresses distributions, are further considered as initial values for the next loading cycle, the incremental technique being reiterated. The cyclic evaluation process of both the plastic strains and residual stresses is performed until the material shakedowns. For the case of cylindrical roller bearings with cylindrical-crowned roller profile, the role played by the crowning geometry on pressure distribution is pointed out for both the elastic analysis and elastic-plastic analysis. Further, the modified rating lives are evaluated using the methodology given in ISO 16281-2008.

In this article we propose a macroscopic model for ferromagnetic hysteresis that is well-suited for finite element implementation. The model is readily vectorial and relies on a consistent thermodynamic formulation. In particular, the stored magnetic energy and the dissipated energy are known at all times, and not solely after the completion of closed hysteresis loops as is usually the case. The obtained incremental formulation is variationally consistent, i.e., all internal variables follow from the minimization of a thermodynamic potential. This variational approach is directly inspired from the kinematic hardening theory of plasticity, which opens the door for novel energy-consistent coupled mechanical/electromagnetic models.

It is well known that the use of inelastic constitutive equations accounting for induced softening leads to pathological space (mesh) and time discretization dependency of the numerical solution of the Initial and Boundary value Problem (IBVP). To solve this drawback a thermodynamically-consistent formulation incorporating first gradient of micromorphic damage in the framework of micromorphic continuum is proposed. In this formulation the damage field is strongly coupled with mixed isotropic and kinematic nonlinear hardening together with micromorphic damage variables. A new finite element with one additional degree of freedom for the micromorphic damage field is developed and implemented into ABAQUS/EXPLICIT using the user’s subroutines VUEL and VUMAT. For the validation purpose, 3D uniaxial tension example of metallic sheet is performed using the proposed micromorphic fully coupled elastoplastic constitutive equations.

This paper presents the application of a viscoplastic damage model for the lifetime prediction of a typical rocket combustion chamber structure. The material modeling is motivated by extension of the classical rheological model for elastoplasticity with Armstrong-Frederick kinematic hardening into a viscoplastic model. The coupling with damage is performed using the concept of effective stress and the principle of strain equivalence. The material parameters are identified based on experimental results for the high temperature copper alloy NARloy-Z, which is one of the typical combustion chamber wall materials. Finally the applicability of the model will be shown by means of sequentially coupled thermomechanical analyses.

In this paper, a finite strain constitutive model for evolving elastic and plastic anisotropy combining nonlinear isotropic and kinematic hardening is presented. The evolution of elastic anisotropy is described by defining the Helmholtz free energy as an isotropic function of a family of evolving structure tensors. In addition, plastic anisotropy is modelled via the dependence of the yield surface on the same family of structure tensors. Exploiting the Clausius-Duhem inequality leads to the interesting result that all tensor-valued internal variables are symmetric. Thus, the integration of the evolution equations can be efficiently performed by means of an implicit algorithm that automatically retains the symmetry of the internal variables in every time step. The material model is used as a user material subroutine UMAT infinite element package ABAQUS/Standard, by means of which the occurrence of earing during cylindrical deep drawing is simulated.

This paper presents the formulation of an advanced mechanical model describing a wide class of anisotropic elastoplastic constitutive equations accounting for the strong coupling with the anisotropic ductile damage. This model is developed within the framework of thermodynamics of irreversible processes with state variables and the continuum damage mechanics. The plastic anisotropy is accounted for through a non-associative theory for which a plasticity yield criterion and the plastic potential are defined separately but considering the strong coupling between both phenomena. The damage anisotropy is defined by using a second rank tensor. The effect of damage on the mechanical fields (stress, hardening, plastic strain, etc…) is described by a fourth rank damage effect operator that is defined in the context of the hypothesis of total energy equivalence. A rotating frame formulation is used to fulfil the objectivity of the constitutive equations under finite transformation. Finally, in order to illustrate the predictive capabilities of the model, the parametric studies with some simple loading case are investigated and the results discussed on the light of the anisotropic character of the ductile damage and its interaction with the anisotropy of plastic flow.

Acoustic emission (AE) has been known as an excellent technique to monitor crack propagation and fracture mechanism. For more domination on AE behavior of materials, comprehensive knowledge on effective parameters is necessary. Heat treatment as one of the important factors on AE characteristics of a material must be considered. This investigation is primarily aimed at studying the effect of tempering heat treatment on characteristics of acoustic emission signals monitored during tension tests of a cold-work tool steel. Single edge notched samples of AISI D2 cold-work tool steel were prepared. Then, respectively annealing, austenitizing and tempering were performed. Tempering was carried out at 5 different temperatures from 0 to 575 C. Finally, samples were loaded at tension and AE signals recorded synergistically. Analyzing of the characteristics of AE signals showed that: (a) In all tempering conditions, the AECC increases slowly at the beginning and rapidly at the point of crack growth, although at higher tempering temperatures we have gradual rise in AECC plot; (b) Increasing tempering temperature, average value of AE count number, amplitude, energy and peak frequency decreases; (c) At 525 C, because of secondary hardening, average value of investigated AE parameters increase strongly and (d) analyzing the relation between fracture mode, AE characteristics and tempering temperature showed that special AE behavior of specimens tempered at 525 C is because of the transformation of retained austenite in ferritic matrix.

In the last decade, instrumented indentation test has been widely used to determine the mechanical properties of different materials and especially for metals. The mechanical properties such as Young modulus, yield stress, hardening exponent, and stress-strain curve were determined with the help of the load–displacement curve of the continuous indentation test. The method consists of pushing an indenter in a material sample and the applied load and the indenter displacement are measured. In this research the load on the indenter was considered as cyclic and varied from zero to F max . Because of the Bauschinger effect, the hysteresis loops were formed. With the help of these hysteresis loops, nonlinear kinematic hardening parameters of the Armstrong–Freiderick (A-F) model can be determined. Spherical indenter was used and the sample was considered isotropic. The material behavior was modeled by the A-F rule. The test was modeled by the finite element method. An axi-symmetric mesh was used. The A–F model constants, C and γ, were varied to obtain their effects on the hysteresis loops. Maximum applied load was considered constant for different finite element modeling and the maximum and residual displacements were calculated from the simulations results. The normalized maximum and the residual displacements were increased as a function of the cycles. It was shown that these parameters value and their rate are dependent on the material model constants. These dependences were shown for different examples which can help to characterize the A-F model constants by the cyclic spherical indentation tests.

In this paper, the dynamic behavior of a quarter-car with two degree-of-freedom which consists of sprung mass and unsprung mass is examined. Nonlinearity occurred due to nonlinear hysteretic suspension damper and spring. Vehicle tire is modeled as a nonlinear hardening spring. The disturbance of road assumed to be sinusoid. Frequency response diagram of the model has been obtained. Results show that the dynamic response of the vehicle can be chaotic. Influence of road roughness amplitude on vehicle vibration is investigated and critical amplitude of the road surface profile is found, above which the system can vibrate chaotically. The comparison between the results obtained from the proposed model and those from the single degree-of-freedom quarter-car model shows that the unsprung mass has great influence on the dynamical behavior of the system, which cannot be ignored.

Fatigue strength is one of the most important mechanical properties. Durability and reliability of car parts are often defined by their fatigue strength, since most of them are loaded with dynamic, repeating or variable loads and the main type of failure is metal fatigue. Various surface hardening methods have a huge impact on fatigue strength of structural materials. The choice of surface processing method is determined by properties and microstructure of a material, as well as the purpose and working conditions of part’s material. Very often the optimum processing is a combination of several methods, which enables to obtain the required properties (high fatigue strength, wear, etc.). The impact of several combined surfaces processing on the fatigue strength of carbon steel samples is investigated in the work. The surface was hardened using different processing combinations: by hardening with high frequency electricity currents, rolling by rollers, heating and cooling under different temperatures. Experimentally it is proved that thermal treatment of plastically deformed carbon steel significantly increases fatigue strength. Experiments showed that after surface hardening with the given regimes, the microstructure and residual stresses are formed in such way that fatigue crack begins to grow under the hardened sample surface.

The behavior of an elastic-plastic contact between a deformable sphere and a rigid flat under combined constant normal and reciprocating tangential loading is investigated theoretically and experimentally. The theoretical model is based on the assumptions of full stick contact condition and elastic–linear kinematic hardening of the sphere material. Hysteretic change of friction force versus tangential displacement during reciprocating tangential loading is investigated along with the study of the change of the contact area and stress state in the elastic-plastic sphere. Good agreement between theoretical and experimental results is obtained.

A numerical solution is presented for a single load-unload cycle of an adhesive contact between an elastic-plastic sphere and a rigid flat. The interacting forces between the sphere and the flat are obtained through connecting non-linear spring elements having force-displacement behavior that obeys the Lennard-Jones potential. Linear kinematic hardening (with tangent modulus of 2% and 5% of the Young’s modulus) rather than isotropic hardening is assumed for the sphere material to account for possible secondary plastification during the unloading. The well known Tabor parameter and a plasticity parameter are shown to be the two main dimensionless parameters governing the problem. The effects of these two parameters on the load-approach curves, on the plastically deformed sphere profiles and on the plastic strain fields inside the sphere are presented, showing different modes of separation during the unloading.

The paper reexamines the extraction of material properties using nanoindentation for linearly elastic and elastic-plastic materials. The paper considers indentation performed using a rigid conical indenter, as follows. Linearly elastic solids : The reduction of nanoindentation test data of elastic solids is usually processed using Sneddon’s relation [1], which assumes a linearly elastic infinite half space and an infinitely sharp indenter tip. These assumptions are violated in practical indentation experiments. Since most of the research on the extraction of material properties relies heavily on numerical simulations, we used them to investigate the specimen dimensions required for it to qualify as an infinite body, and the indentation conditions for finite tip radius effect to be negligible. The outcome of this part is firstly, the definition of a “converged” 2D geometry so that additional magnification of the numerical model does not influence the load-displacement curve, and secondly, an explicit relationship between the measured load and displacement that takes into account the finite tip radius. Elastic-plastic solids : Here, the main data reduction technique was proposed by Pharr et al. [2], assuming elastic unloading of a plastic nanoindentation. We investigated the effects of finite tip radius in elastic-plastic indentations and found that the accuracy of the prediction is currently limited by the accurate determination of the projected contact area. This point will be discussed and a new experimental technique to measure the projected contact area will be proposed. The Poisson’s ratio effect in elastic-plastic indentations is found to be different from the linearly elastic case. This leads to the discussion on the applicability of the correction factor (for Poisson’s ratio effect) derived in linear elastic indentations, on elastic-plastic indentations. Finally, a technique to obtain an upper bound estimate of the yield stress for the indented elastic-plastic material (which is an exact estimation for non-hardening materials), will be presented.

In the present study, the nonlinear dynamic response of clamped immovable oval cylindrical shells subjected to radial harmonic excitation in the spectral neighborhood of the free vibration frequency is investigated. The formulation is based on the first order shear deformation theory. Geometric nonlinearity is inducted in the formulation considering moderately large deformation effects employing the Sanders type kinematic relations. Governing equations are discretized in space and time domains, respectively, employing computationally efficient finite-strip method and Newmark time marching scheme. Resulting nonlinear algebraic equations are solved using Newton-Raphson iterative technique. A detailed parametric study is conducted to bring out the influence of ovality parameter on the nonlinear vibration characteristics of different modes of vibrations of isotropic and angle-ply oval shells. For isotropic oval shells, it is observed that moderately oval shells show softening type nonlinearity whereas shells of large ovality show hardening type nonlinearity. The response of oval shells with large ovality reveals different temporal variation near to the semi-major axis region compared to that in the semi-minor axis region.

Mechanical behavior of crystals is dictated by dislocation motion in response to applied force. While it is extremely difficult to directly observe the motion of individual dislocations, several correlations can be made between the microscopic stress-strain behavior and dislocation activity. Here, we present for the first time the differences observed between mechanical behavior in two fundamental types of crystals: face-centered cubic, fcc (Au, Cu, Al, Ni, etc.) and body-centered cubic, bcc (W, Cr, Mo, Nb, etc.) with sub-micron dimensions subjected to in-situ micro-compression in SEM chamber. In a striking deviation from classical mechanics, there is a significant increase in strength as crystal size is reduced to 100nm; however in gold crystals (fcc) the highest strength achieved represents 44% of its theoretical strength while in molybdenum crystals (bcc) it is only 7%. Moreover, unlike in bulk where plasticity commences in a smooth fashion, both nano-crystals exhibit numerous discrete strain bursts during plastic deformation. These remarkable differences in mechanical response of fcc and bcc crystals to uniaxial micro-compression challenge the applicability of conventional strain-hardening to nano-scale crystals. We postulate that they arise from significant differences in dislocation behavior between fcc and bcc crystals at nanoscale and serve as the fundamental reason for the observed differences in their plastic deformation. Namely, dislocation starvation is the predominant mechanism of plasticity in nano-scale fcc crystals while junction formation and subsequent hardening characterize bcc plasticity, as confirmed by the microstructural electron microscopy. Experimentally obtained stress-strain curves together with video frames during deformation and cross-sectional TEM analysis are presented, and a statistical analysis of avalanche-like strain bursts is performed for both crystals and compared with stochastic models.

An analysis model has been developed to model the nonlinear strain rate dependent deformation of rolling bearing steel stressed in the elastic-plastic domain. The model is developed in the frame of the incremental theory of plasticity by using the von Mises yield criterion and Prandtl-Reuss equations. By considering the isotropic and non-linear kinematic hardening laws of Lemaitre-Caboche, the model accounts for the cyclic hardening phenomena. To attain the final load of each loading cycle, the two bodies are brought into contact incrementally. For each new load increment new increments for the components of stress and strain tensors, but also increments of residual stresses, are computed for each point of the 3D mesh. Both, the new contact geometry and residual stresses distributions, are further considered as initial values for the next loading cycle, the incremental technique being reiterated. The cyclic evaluation process of both, plastic strains and residual stresses is performed until the material shakedowns. The experimental part of the paper regards to the rolling contact fatigue tests carried out on two groups of line contact test specimens and on two groups of deep groove ball bearings. In both cases, the experimental data reveal more than two times greater fatigue life for the group with induced residual stresses versus the life of the reference group. The von Mises equivalent stress is considered in Ioannides-Harris rolling contact fatigue model to obtain theoretical lives. The theoretical analysis revealed greater fatigue lives for the test specimens and for the ball bearings groups with induced residual stresses than the fatigue lives of the corresponding reference groups.

In this paper a corotational constitutive model for the large elastoplastic deformation of hardening materials using subloading surface model is formulated. This formulation is obtained by refining the large deformation theory of Naghdabadi and Saidi (2002) adopting the corotational logarithmic (Hencky) strain rate tensor and incorporating it into the subloading surface model of Hashiguchi (1980, 2003) falling within the framework of the unconventional plasticity. As an application of the proposed constitutive model, the large Elastoplastic deformation of simple shear example has been solved and the results have been compared with classical elasto-plastic model using the Hencky strain tensor. Also the effect of the choice of corotational rates on stress components has been studied.

In this paper, based on the multiplicative decomposition of the deformation gradient tensor an elastic-plastic modeling of kinematic hardening materials is introduced. In this model, the elastic constitutive equation as well as the flow rule and hardening equation are expressed in terms of the corotational rate of the elastic and plastic logarithmic strains. As an application, the simple shear problem is solved and the stress components are plotted versus shear displacement for a kinematic hardening material.

The kinematic hardening theory of plasticity based on the Prager model and incremental isotropic damage is used to evaluate the cyclic loading behavior of a beam under the axial, bending, and thermal loads. This allows damage to be path-dependent. The damage and inelastic deformation are incorporated and they are used for the analysis of the beam. The beam material is assumed to follow linear strain hardening property coupled with isotropic damage. The material strain hardening curves in tension and compression are assumed to be both identical for the isotropic material. Computational aspects of rate independent model is discussed and the constitutive equation of the rate independent plasticity coupled with the damage model are decomposed into the elastic, plastic and damage parts. Return Mapping Algorithm method is used for the correction of the elastoplastic state and for the damage model the algorithm is used according to the governed damage constitutive relation. The effect of the damage phenomenon coupled with the elastoplastic kinematic hardening is studied for deformation and load control loadings.