Extended overstress model and its implicit stress integration algorithm: Formulations,experiments, and simulations

The extended overstress model is formulated based on the subloading surface model with the smooth elastic-inelastic transition, which is called the subloading-overstress model. Therein, the rigorous translation rules of the elastic-core and the similarity-center, the limitation in the expansion of the subloading surface, and so forth are incorporated. The model possesses the basic structure capable of describing the monotonic/cyclic loading behaviors at the general rate of deformations from the quasi-static to the impact loading. The experiments were conducted using the spheroidal graphite cast iron under the various loading conditions. It was verified that the experimental results can be simulated accurately by the subloading-overstress model. Further, the complete implicit stress integration algorithm based on the return-mapping projection is formulated for the present subloading-overstress model and implemented into Abaqus through UMAT. Then, the deformation analyses of the R-notched cylinder were performed by the present algorithm. Consequently, the performability of the present algorithm is verified by the analyses of the boundary-value problem under the cyclic loadings.     

Closest-point projection method for the extended subloading surface model

This paper presents an implicit integration scheme based on the closest-point projection method for an unconventional plasticity model, the extended subloading surface model. A cutting-plane algorithm has already been formulated for the model. However, the present paper aims to introduce an alternative closest-projection return mapping scheme for resolving the elasto-plastic problem by improving the accuracy of the similarity center variable. Numerical examples are examined for monotonic and cyclic loading conditions to validate the results against a forward Euler method. The speed and accuracy of the resolution technique are determined, showing the local and global convergence rates and the iso-error map for the numerical algorithm.     

An analysis of a new class of integration algorithms for elastoplastic constitutive relations

An accuracy analysis of a new class of integration algorithms for finite deformation elastoplastic constitutive relations recently proposed by the authors, is carried out in this paper. For simplicity, attention is confined to infinitesimal deformations. The integration rules under consideration fall within the category of return mapping algorithms and follow in a straightforward manner from the theory of operator splitting applied to elastoplastic constitutive relations. General rate-independent and rate-dependent behaviour, with plastic hardening or softening, associated or non-associated flow rules and nonlinear elastic response can be efficiently treated within the present framework. Isoerror maps are presented which demonstrate the good accuracy properties of the algorithm even for strain increments much larger than the characteristic strains at yielding.     

A new soft-particle DEM model of micro-particle impact integrated adhesive,elastoplastic and microslip behaviors

Micro-particle impact is a problem of solid mechanics that is common in many applications. To address this problem, a new soft-particle DEM model of micro-particle impact is proposed, which incorporates adhesive, elastoplastic and microslip behaviors. The normal force model is developed as two contiguous loading stages: the elastic stage and the elastoplastic stage in which the transition is from the elastic deformation to fully plastic deformation. Most innovative in unloading, the normal force model is also evolved into two contiguous stages: unloading under elastic loading and unloading under elastoplastic loading in which it combines Hertz elastic model and Mesarovic-Johnson plastic model. The normal force model is further assumed as the one-way coupling with pressure-based Maw tangential model with the micro-slip behavior. Further model validations are performed by employing the experimental results in literatures. The validation results indicate that model predictions agree with the experimental data, and are demonstrated to be incredibly accurate than other models, particularly for restitution coefficients and critical sticking velocity. Furthermore we can find that the smaller size particle has a longer period of nonlinear loading, while the larger size particle has a longer period of linear loading. For tangential restitution coefficient at the small incident angle, a down trend may be due to the oscillation of the tangential force.     

Monotonic and Cyclic Deformations of Case‐Hardened Steels Including Residual Stress Effects

Abstract: Monotonic and cyclic deformations of case‐hardened steel specimens under axial loading were investigated experimentally and analytically. A finite element (FE) model for the case‐hardened specimens was constructed to study multiaxial stresses due to different plastic flow behaviour between the case and the core, as well as to evaluate residual stress relaxation and redistribution subsequent to cyclic loading. The multiaxial stress is shown to increase the effective stress on the surface, and, therefore, unfavourable to yielding or fatigue crack nucleation. The residual stresses are shown to relax or redistribute, even in the elastic‐behaving region, when any part of a case‐hardened specimen or component undergoes plastic deformation. Multi‐layer models were used to analyse and predict monotonic and cyclic deformation behaviours of the case‐hardened specimen based on the core and case material properties, and the results are compared with the experimental as well as FE model results. The predicted monotonic stress–strain curves were close to the experimental curves, but the predicted cyclic stress–strain curves were higher than the experimental curves.     

EXPONENTIAL MAP ALGORITHM FOR STRESS UPDATES IN ANISOTROPIC MULTIPLICATIVE ELASTOPLASTICITY FOR SINGLE CRYSTALS

This paper presents a new stress update algorithm for large-strain rate-independent single-crystal plasticity. The theoretical frame is the well-established continuum slip theory based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts. A distinct feature of the present formulation is the introduction and computational exploitation of a particularly simple hyperelastic stress response function based on a further multiplicative decomposition of the elastic deformation gradient into spherical and unimodular parts, resulting in a very convenient representation of the Schmid resolved shear stresses on the crystallographic slip systems in terms of a simple inner product of Eulerian vectors. The key contribution of this paper is an algorithmic formulation of the exponential map exp: sl(3) → SL(3) for updating the special linear group SL(3) of unimodular plastic deformation maps. This update preserves exactly the plastic incompressibility condition of the anisotropic plasticity model under consideration. The resulting fully implicit stress update algorithm treats the possibly redundant constraints of single-crystal plasticity by means of an active set search. It exploits intrinsically the simple representation of the Schmid stresses by formulating the return algorithm and the associated consistent elastoplastic moduli in terms of Eulerian vectors updates. The performance of the proposed algorithm is demonstrated by means of a representative numerical example.     

Failure assessment of a hard brittle coating on a ductile substrate subjected to cyclic contact loading

Hard brittle films and coatings are often employed as a protective coating for metallic ductile substrates. In use, such coatings are generally subjected to cyclic/repeated contact loading and sliding over long periods of time. This study investigated the monotonic and cyclic contact fracture mechanism of hard coatings on ductile substrates (an electroplated Ni–P coating on a stainless steel substrate, SUS304) in order to evaluate their mechanical durability. In the experiment, both monotonic and cyclic indentation tests using a ball indenter with large contact force were performed. The fracture nucleation process was identified using the acoustic emission method. For monotonic contact loading (single indentation), coating cracks are produced by the excessive plastic deformation of the substrate, itself caused by contact loading, which makes the bending curvature of a coating a critical moment. Subsequently, cyclic contact loading (cyclic indentation) was applied to the coating in order to investigate the cycle number of film cracking. It was found that the critical contact force for coating fracture decreases, compared with that of monotonic loading. This critical force is dependent on the number of loading cycles. This may be due to the fact that cyclic contact loading encourages large plastic deformation of the SUS304 substrate owing to cyclic plasticity. Therefore, the cyclic plastic deformation behavior of the substrate was investigated using cyclic microindentation tests and the finite element method. In the computation, the Chaboche model was employed to compute the cyclic plastic deformation of the substrate, since it simulates cyclic plasticity. We clarified the cyclic contact fracture mechanism of electroplated Ni–P coating on an SUS304 substrate. Based on this, we finally predicted the coating lifetime (i.e., mechanical durability) under cyclic contact loading. Therefore, the present study is useful for obtaining information about film/coating fracture properties under both monotonic and cyclic contact loadings.     

Fractographic and numerical study of hydrogen–plasticity interactions near a crack tip

This paper offers a fractographic and numerical study of hydrogen–plasticity interactions in the vicinity of a crack tip in a high-strength pearlitic steel subjected to previous cyclic (fatigue) precracking and posterior hydrogen-assisted cracking (HAC) under rising (monotonic) loading conditions. Experiments demonstrate that heavier cyclic preloading improves the HAC behaviour of the steel. Fractographic analysis shows that the microdamage produced by hydrogen is detectable through a specific microscopic topography: tearing topography surface or TTS. A high resolution numerical modelling is performed to reveal the elastoplastic stress–strain field in the vicinity of the crack tip subjected to cyclic preloading and subsequent monotonic loading up to the fracture instant in the HAC tests, and the calculated plastic zone extent is compared with the hydrogen-assisted microdamage region (TTS). Results demonstrate that the TTS depth has no relation with the active plastic zone dimension, i.e., with the size of the only region in which there is dislocation movement, so hydrogen transport cannot be attributed to dislocation dragging, but rather to random-walk lattice diffusion. It is, however, stress-assisted diffusion in which the hydrostatic stress field plays a relevant role. The beneficial effect of crack-tip plastic straining on HAC behaviour might be produced by the delay of hydrogen entry caused by residual compressive stresses and by the enhanced trapping of hydrogen as a consequence of the increase of dislocation density after cyclic plastic straining.     

Contact damage in an yttria stabilized zirconia: Implications

This paper presents the results of a combined experimental and computational study of contact damage in a 3 mole% yttria partially stabilized zirconia (3-YSZ) that is relevant to hip implants and dental restorations. Contact-induced loading in real applications is idealized using Hertzian contact model to explain plasticity phenomena and failure mechanisms observed under monotonic and cyclic loading. Under monotonic loading, the elastic moduli increase with increasing loading levels. Under cyclic loading, the ceramic specimens fail with progressive cone cracking. X-ray analyses reveal that stress-induced phase transformation (from tetragonal to monoclinic phases) occurs under cyclic contact loading above the critical load levels (~8.5 kN). Furthermore, when the cyclic loading level (5.0 kN) is less than a critical load levels (7.5 kN) that is required to induce surface cone cracks, significant plastic damage is observed in the subsurface zone underneath the contact area. These suggest that the cyclic contact loading induce both plastic damage and tetragonalto-monoclinic phase transformation in the 3-YSZ, leading to significant degradation in long-term strength. The implications of the results are discussed for the design of zirconia femoral heads in total hip replacements and zirconia crowns in dental restoration.     

基于SMP破坏准则的土体弹塑性动力本构模型

利用土体的塑性流动理论,提出了用于描述饱和砂土动力反应性质的弹塑性本构模型。土体总的变形由三部分组成:即弹性应变、与体积屈服机制相关的塑性应变和与剪切屈服机制相关的塑性应变。土体在初始加载与卸载和重新加载阶段性质的差别通过采用不同的模型参数加以反映。该模型能够较为准确地描述饱和砂土在单调加载和循环加载条件下的反应性质。     

弹塑性随机有限元在低周疲劳分析中的应用

推导了交变载荷下弹塑性随机有限元的迭代格式,计算了局部多轴应力应变的随机响应。迭代格式中,针对复杂的交变载荷,采用运动强化模型反映塑性变形引起的各向异性和包辛格效应,运用Jhansale模型描述材料的瞬态应力应变关系。弹塑性有限元分析,克服了以往近似方法只能计算单轴局部应力应变响应的缺陷,为多轴疲劳分析奠定了基础。考虑零构件的随机因素,将随机有限元方法引入到交变载荷下弹塑性有限元的迭代格式中,得到局部应力应变的随机响应,为低周疲劳可靠性分析提供了更精确的依据。MontCarlo模拟结果证实了提出的弹塑性随机有限元方法是可靠的。     

Floating stress‐point integration meshfree method for large deformation analysis of elastic and elastoplastic materials

A new meshfree formulation of stress‐point integration, called the floating stress‐point integration meshfree method, is proposed for the large deformation analysis of elastic and elastoplastic materials. This method is a Galerkin meshfree method with an updated Lagrangian procedure and a quasi‐implicit time‐advancing scheme without any background cell for domain integration. Its new formulation is based on incremental equilibrium equations derived from the incremental virtual work equation, which is not generally used in meshfree formulations. Hence, this technique allows the temporal continuity of the mechanical equilibrium to be naturally achieved. The details of the new formulation and several examples of the large deformation analysis of elastic and elastoplastic materials are presented to show the validity and accuracy of the proposed method in comparison with those of the finite element method. Copyright © 2012 John Wiley & Sons, Ltd.     

Numerical investigation of crack tip strain localization under cyclic loading in FCC single crystals

In this work, the crack tip strain localization in a face centered cubic single crystal subject to both monotonic and cyclic loading was investigated. The effect of constraint was implemented using T-stress and strain accumulation was studied for both isotropic and anisotropic elastic cases with the appropriate application of remote displacement fields in plane strain. Modified boundary layer simulations were performed using the crystal plasticity finite element framework. The consideration of elastic anisotropy amplified the effect of constraint level on stress and plastic strain fields near the crack tip indicating the importance of its use in fracture simulations. In addition, to understand the cyclic stress and strain behavior in the vicinity of the crack tip, combined isotropic and kinematic hardening laws were incorporated, and their effect on the evolution of yield curves and plastic strain accumulation were investigated. With zero-tension cyclic load, the evolution of plastic strain and Kirchhoff stress components showed differences in magnitudes between isotropic and anisotropic elastic cases. Furthermore, under cyclic loading, ratcheting was observed along the localized slip bands, which was shown to be affected by T-stress as well as elastic anisotropy. Negative T-stress increased the accumulation of plastic strain with number of cycles, which was further amplified in the case of elastic anisotropy. Finally, in all the cyclic loading simulations, the plastic strain accumulation was higher near the \(55^0 \) slip band.     

Finite element simulation of plasticity induced crack closure with different material constitutive models

The study presented in this paper analyses the mechanical effects of material constitutive modelling on the numerical prediction of plasticity induced crack closure. With this aim, an elastoplastic stress analysis of a MT specimen was conducted using an implicit three dimensional finite element program. Two materials were studied: an Aluminium Alloy and a High Strength Steel. Several constitutive models were used to describe their cyclic behaviour, ranging from pure isotropic hardening or pure kinematic hardening models to combined isotropic plus kinematic hardening models. Numerical results showed clear differences in plastic behaviour and crack closure predictions for the different types of mechanical models used to describe the mechanical behaviour of the materials. The mechanisms of opening stress stabilization, usually observed in numerical simulations, are explained in this work by analysing the evolution of plastic deformation along the crack flanks. The same type of plastic deformation stabilization behaviour was observed independently of the hardening model in use.     

A nonlocal lattice particle model for J2 plasticity

In virtue of their intrinsic integro-differential formulation of underlying physical behavior of materials, discontinuous computational methods are more beneficial over continuum-mechanics-based approaches for materials failure modeling and simulation. However, application of most discontinuous methods is limited to elastic/brittle materials, which is partially due to their formulations are based on force and displacement rather than stress and strain measures as are the cases for continuous approaches. In this article, we formulate a nonlocal maximum distortion energy criterion in the framework of a lattice particle model for modeling of elastoplastic materials. Similar to the maximum distortion energy criterion in continuum mechanics, the basic idea is to decompose the energy of a discrete material point into dilatational and distortional components, and plastic yielding of bonds associated with this material point is assumed to occur only when the distortional component reaches a critical value. However, the formulated yield criterion is nonlocal since the energy of a material point depends on the deformation of all the bonds associated with this material point. Formulation of equivalent strain hardening rules for the nonlocal yield model was also developed. Compared to theoretical and numerical solutions of several benchmark problems, the proposed formulation can accurately predict both the stress-strain curves and the deformation fields under monotonic loading and cyclic loading with different strain hardening cases.     

An experimental methodology for characterizing fracture of hard thin films under cyclic contact loading

Hard thin films are often employed as protective coatings for metal substrates and their fatigue/fracture property (especially that under contact) needs to be sufficiently understood. In this study, we present a combined experimental/computational framework for exploring the fracture characteristics of hard thin films upon both monotonic and cyclic contacts. The techniques of acoustic emission and corrosion potential fluctuation are combined to monitor the mode and initiation of crack, and numerical simulations based on the finite element method provide further information on the criterion of film fracture. For a model system of a TiN film physical vapor deposited onto a stainless steel substrate, ring cracks are produced when the stress in the film exceeds critical — such a critical moment arrives when the substrate undergoes excessive deformation, which makes the curvature of film bending critical just outside the contact zone. Since cyclic contact loading encourages large plastic deformation of substrate due to ratcheting plasticity, it is found that the critical contact force degrades, compared with monotonic loading. The present experimental/computational methodology is useful for obtaining the information of film fracture property under both monotonic and cyclic contact loads.     

Development of new cyclic plasticity model for 304LN stainless steel through simulation and experimental investigation

Cyclic plastic deformation characteristics of 304LN stainless steel material have been studied with two proposed cyclic plasticity models. Model MM-I has been proposed to improve the simulation of ratcheting phenomenon and model MM-II has the capability to simulate both cyclic hardening and softening characteristics of the material at various strain ranges. In the present paper, strain controlled simulations are performed with constant, increasing and decreasing strain amplitudes to verify the influences of loading schemes on cyclic plasticity behaviors through simulations and experiments. It is observed that the material 304LN exhibits non Masing characteristics under cyclic plastic deformation. The measured deviation from Masing is well established from the simulation as well as from experiment. Simulation result shows that the assumption of only isotropic hardening is unable to explain the hardening or softening characteristics of the material in low cycle fatigue test. The introduction of memory stress based cyclic hardening coefficient and an exponentially varying ratcheting parameter in the recall term of kinematic hardening rule, have resulted in exceptional improvement in the ratcheting simulation with the proposed model, MM-II. Plastic energy, shape and size of the hysteresis loops are additionally used to verify the nature of cyclic plasticity deformations. Ratcheting test and simulation have been performed to estimate the accumulated plastic strain with different mean and amplitude stresses. In the proposed model MM-I, a new proposition is incorporated for yield stress variation based on the memory stress of loading history along with the evolution of ratcheting parameter with an exponential function of plastic strain. These formulations lead to better realization of ratcheting rate in the transient cycles for all loading schemes. Effect of mean stress on the plastic energy is examined by the simulation model, MM-I. Finally, the micro structural investigation from transmission electronic microscopy is used to correlate the macroscopic and microscopic non Masing behavior of the material.     

FE analysis of residual stress relaxation in a girth-welded duplex stainless steel pipe under cyclic loading

This study intends to characterize the residual stress relaxation in a girth-welded duplex stainless steel pipe exposed to cyclic loading. FE thermal simulation of the girth welding process is first performed to identify the weld-induced residual stresses. 3-D elastic–plastic FE analyses incorporated with the cyclic plasticity constitutive model which can describe the cyclic stress relaxation are next carried out to evaluate reconstruction of the residual stresses under cyclic mechanical loading. The results unveils that considerable reduction of the residual stresses in and around the girth weld occur even after the initial few loading cycles and degree of the stress relaxation is dependent on the magnitude of applied cyclic loading.