Viscoplastic Analysis Research Articles

Practical aspects of thermomechanical modeling in electronics packaging: A case study with a SiC power package

In this paper, we presented several practical aspects for building robust and reliable finite element models in thermomechanical modeling in electronics packaging using finite element analysis. Firstly, for layered or patterned structures, a homogenized equivalent model, with equivalent orthotropic material properties, gives excellent agreement with the exact finite element model solutions. Such a simplified finite element model provides an efficient way for structural parameter optimization. Secondly, the finite element mesh should keep the fixed size and shape at the location of interest where the singular point exists. This approach provides a simple way for relative stress comparison in different designs, although the absolute value of stress components has no actual meaning. Thirdly, to further eliminate the mesh dependency, the volume averaging method can be used. We extended the local volume averaging method for large-area die attach problems. Fourthly, in this paper, we presented a comparison study between linear elastic and nonlinear viscoplastic analysis, and demonstrated that in some cases, two different types of analysis give opposite trend results. Lastly, we demonstrated that with the use of different stress components, the conclusions may be different. We also provided an ANSYS APDL script in the supplemental material as a benchmark example.

Microscale viscoplastic analysis of unidirectional CFRP composites under the influence of curing process

Cure-induced residual stresses have a great impact on the mechanical behavior of carbon fiber reinforced polymer (CFRP) composites. This paper develops an integrated analytical framework to study the effect of the cure-induced residual stresses on the mechanical behavior of unidirectional IM7/8552 composites. During the curing process, evolution of the material properties of the resin matrix is captured using the cure hardening instantaneous linear elastic (CHILE) model. In addition to the mechanical strain, thermal and chemical shrinkage strains of the resin are taken into account in the determination of the residual stresses. By introduction of the predicted residual stresses into the representative volume element (RVE), the quasi-static and dynamic compression analyses are performed to demonstrate the local viscoplastic deformation of the matrix and the homogenized stress–strain response of the composites. Simulation results are in good agreement with the experimental data. The comparative analysis indicates that the cure-induced residual stresses lead to an earlier nonlinearity and lower compressive strength. Furthermore, to investigate the effect of the fiber distribution on the residual stresses and compressive response of the composites, a parametric analysis is performed, in which two parameters are considered, i.e., minimal inter-fiber distance and fiber volume fraction.

Viscoplastic analysis method of an aeroengine turbine blade subjected to transient thermo-mechanical loading

Viscoplastic analysis method of a turbine blade manufactured with directionally solidified (DS) superalloy under transient thermo-mechanical loading was investigated in depth. The second deviatoric stress tensor invariant was modified by a fourth-order tensor to simulate the anisotropic behavior of the DS superalloy. In order to capture the monotonic and cyclic behaviors of the alloy under non-isothermal conditions, temperature interpolation of a set of material parameters and the modification of internal state variables were performed. The model was implemented as a user subroutine (UMAT) in Abaqus for complex structure analysis. With the improved Chaboche constitutive model, the tensile and cyclic responses of the DS material GTD-111 under isothermal and non-isothermal conditions were carefully modeled and predicted with high accuracy. Finally, the model was implemented to simulate the transient thermo-mechanical behavior of a hollow turbine blade with a typical flight profile. The location-dependent thermo-mechanical fatigue response of the blade were determined and analyzed.

Simulation of buckling of internal features during selective laser sintering of metals

Additive manufacturing (AM) processes, such as Selective Laser Sintering (SLS), have enabled the fabrication of geometrically complicated designs. However, undesired distortions due to thermally-induced residual stresses may lead to loss of tolerance or failure of the part. One potential failure mode is buckling, particularly when realizing high aspect ratio features, like for infill, to minimize weight. In this paper, we address distortions and part failures due to buckling by using a finite element model to predict residual stress distributions and sintering induced distortions. Initially, we conduct a transient thermal simulation to determine the Heat Affected Zone (HAZ), which is then used in the thermomechanical simulation. In addition, we imposed perturbations on the mechanical mesh based on the buckling eigenmodes. Finally, a thermomechanical viscoplastic analysis was performed layer-by-layer to obtain the final residual stress state and subsequent distortions that occur after cooling down to ambient temperature. A model was used to describe the evolution of porosity due to laser sintering, and then a model of the effects of porosity on the viscoplastic constitutive properties of the sintered material was used in the thermomechanical simulation. Modeling results are compared against experimental specimens using a Durelli (aka, Theta) specimen geometry fabricated with a 3D Systems ProX 200 Selective Laser Sintering (SLS) machine. The geometry of the specimen represents an internal feature with a high aspect ratio that is prone to buckling, and the dimensions were modified based on the simulation results to confirm the ability of the modeling approach to provide accurate mitigation of buckling-induced distortions.

High-order virtual element method for the homogenization of long fiber nonlinear composites

A high-order virtual element method (VEM) for homogenization of long fiber reinforced composites is presented. In particular, periodic composites are considered studying square or rectangular unit cell arrays and circular inclusions. A suitable displacement representation form is adopted reducing the three-dimensional problem to an equivalent two-dimensional one. Material nonlinearity is taken into account for the matrix which can be plastic or visco-plastic. The formulation is proposed for linear and high-order virtual elements. Numerical applications are performed to assess the accuracy of the VEM formulation in comparison with the classical finite element approach. In particular, convergence investigations on the overall elastic moduli and on the Mises equivalent stress are performed. Elasto-plastic and visco-plastic analyses are carried out exploiting the local mesh refinement features typical of VEM showing efficiency of polygonal discretizations.

Cyclic viscoplastic analysis for steam generator material of Indian fast breeder reactor

AbstractCreep‐fatigue interaction behavior of grade 91 steel at 823 K has been studied. Creep component has been introduced with hold times 1, 10, and 30 minutes in tension and compression in continuous strain cycling. Fatigue life reduced due to application of hold and reduction was found to be more in compressive hold. The effect of various factors such as mean stress, stress relaxation, oxidation, microstructure, and inelastic strain accumulation on significant reduction in fatigue life in compression hold has been investigated. The oxidation has been observed as the key parameter that caused significant fatigue life reduction in compressive hold as compared with tensile hold. Chaboche unified viscoplasticity model has been used to understand the material's cyclic elasto‐viscoplastic behavior. The simulation results were in agreement with the experimental results. Fatigue lives under creep‐fatigue condition were estimated using frequency‐modified strain energy damage function method and linear damage summation method. Frequency‐modified strain energy damage function method under estimated the fatigue lives whereas linear damage summation method overestimated the lives.

An efficient load identification for viscoplastic materials by an inverse meshfree analysis

Despite the extensive study of direct viscoplastic analysis in the past, its inverse study has remained very scarce indeed. In this paper, an inverse method based on an improved version of the meshfree radial point interpolation method (RPIM) is presented for load identification in 2D viscoplasticity. The unknown load, varying with respect to space and time, is determined using measured strains at several sampling points on boundary or within the domain of the problem. The inverse analysis employs the well-known Tikhonov regularization and damped Gauss–Newton methods. Proper location and arrangement of sampling points for more accurate identification of unknowns is investigated too. To demonstrate the feasibility of the proposed method, a comprehensive numerical example in different conditions is presented. Furthermore, the effects of some important parameters, such as the number of sampling points and measurement errors, on the stability and accuracy of the solution are also studied.

Unified viscoplasticity modelling and its application to fatigue-creep behaviour of gas turbine rotor

This paper presents an elasto-viscoplastic finite element modelling framework including the associated UMAT codes to investigate the high-temperature behaviour of a gas turbine rotor steel. The model used in the FE study is an improved and unified Chaboche–Lemaitre model which combines a power flow rule with non-linear anisothermal evolution of isotropic and kinematic hardening. The computational methodology is a three-dimensional framework following an implicit formulation and based on a radial return mapping algorithm. The UMAT is calibrated and validated across isothermal hold-time cyclic tests. The model is applied to a classical industrial gas turbine rotor to study the spatial heterogeneities and critical high stress areas within the rotor structure. The effect of thermal transients and geometry singularities on the development of residual stresses is underlined. Finally, the potential improvements and extensions of such FE viscoplastic analysis are discussed.

A Numerical Comparison of the Behavior of a Braced Excavation Using Two and Three-Dimensional Creep Plastic Analyses

Current study deals with investigating the effects of both time factor and the selection of a constitutive model type on predicting deformations of an excavation braced by nailing using two and three-dimensional finite element analyses. In addition, the effects of stress path and the type of defined initial conditions of the analytical model on deformations of the floor and walls of the excavation are also studied. Time factor, in the form of earth materials’ creep, can largely be entered into calculation of deformations of excavations by conducting viscoelastic and viscoplastic analyses. On the other hand, there hasn’t been done a comprehensive study regarding the creep behavior of excavations through comparing the results of two-dimensional and three-dimensional numerical analyses so far. The results showed that it’s largely possible to approach the actual deformation behavior of an excavation by considering the constitutive model of soft soil creep, SSC model, in the numerical plastic analyses. The effects of stress path on the deformation behavior of the excavation walls and excavation floor are investigated by using OCR stress ratio and POP stress difference; These two factors, both of which are also analogous, represent a boundary value for swelling behavior of the excavation floor and an increasing rate for the deformation behavior of the excavation walls since the increase in OCR or POP is equal to the increase in the soil lateral pressure coefficient at rest.

Linear and nonlinear viscoelastic and viscoplastic analysis of asphalt binders with warm mix asphalt additives

ABSTRACTWarm-Mix Asphalt (WMA) is a widely used product, which proved a contribution to the reduction in asphalt mixing and compaction temperatures. This reduction leads to lower fuel consumption and smoke emission in asphalt plants. Most of the characterisation of binders used in WMA has focused in the past on measuring linear viscoelastic properties and associated Superpave parameters. Several studies have shown that the average stresses and strains of the asphalt mixture remain mostly within the linear viscoelastic response. However, localised strains in the binder phase of the mixture could reach values high enough to induce nonlinear viscoelastic and viscoplastic deformations. Therefore, this study focuses on an experimental and analytical evaluation of linear, nonlinear viscoelastic and viscoplastic responses of selected binders modified for use in WMA. The first part of the paper analyses the linear viscoelastic material properties and their ability to evaluate permanent deformation resistance. Then, the non-recoverable creep compliance parameter obtained from the Multiple Stress Creep Recovery (MSCR) test is analysed to assess the nonlinear response and permanent deformation of asphalt binders. The paper utilises a nonlinear plasto-viscoelastic (NPVE) approach to assess and quantify the nonlinear plasto-viscoelastic response of binders by separating the recoverable and irrecoverable strains measured in the MSCR test. Two WMA additives were included in this study by mixing them with polymer-modified and unmodified asphalt binders. Analysis of results showed that the NPVE approach captured a higher percentage of recovery than the NLVE approach. However, binder’s performance evaluation and ranking did not change by adopting the NPVE approach. The nonlinear viscoelastic parameters provided insight on the behaviour of asphalt binders mixed with WMA additives during loading cycles. Sasobit showed higher influence than Advera on binders in resisting permanent deformation by increasing the recoverable strain during the unloading phase.

Reply to the discussion by Mesri and Wang on “Large-strain elastic viscoplastic consolidation analysis of very soft clay layers with vertical drains under preloading”

The design of preloading involves loading schedule design and prediction of post-construction settlement. As the in situ measurement data are usually unavailable during the loading schedule design, it is difficult to estimate the preloading effects before construction. In this Reply, we first discuss the satisfied conditions of eq. (D4) in the Discussion (Mesri andWang 2015) based on Bjerrum’s creep diagram (Bjerrum 1967) and Yin–Graham’smodel (Yin and Graham 1989). Then the research objective and significance of the paper under discussion (Hu et al. 2014) are addressed. Based on Bjerrum’s creep diagram and Yin–Graham’s model, the void ratio at the end of service period for soft soil can be expressed as (Hu 2012)

Discussion of “Large-strain elastic viscoplastic consolidation analysis of very soft clay layers with vertical drains under preloading”

where vs ′ and vf ′ are the effective vertical stress reached before the removal of surcharge and final effective vertical stress, respectively. According to the observed ground surface settlements in Fig. 9 and the pore-water pressure measurements in Fig. 10, end of primary (EOP) consolidation was probably reached near 610 days when the 20 kPa surcharge was removed. The post-surcharge secondary settlement is computed using (Terzaghi et al. 1996, p. 110)

Negative through-the-thickness Poisson’s ratio of elastic–viscoplastic angle-ply carbon fiber-reinforced plastic laminates: Homogenization analysis

Negative through-the-thickness Poisson’s ratios are investigated macroscopically and microscopically in the elastic–viscoplastic behavior of angle-ply carbon fiber-reinforced plastic (CFRP) laminates. For this purpose, an analysis method is proposed based on a homogenization theory for nonlinear time-dependent composites with point-symmetric internal structures. This method is able to efficiently analyze both the macroscopic and microscopic elastic–viscoplastic properties of angle-ply CFRP laminates fully modeled with microstructures consisting of fibers and a matrix. Using the proposed method, the elastic–viscoplastic analysis of angle-ply carbon fiber/epoxy laminates with various laminate configurations is performed to investigate their Poisson’s ratios in the viscoplastic region. It is revealed that, for a range of laminate configurations, the through-the-thickness Poisson’s ratios exhibit negative values which become increasingly negative as the viscoplastic deformation progresses in the laminates. The effect of strain rate on this increasing negativity is also demonstrated, and microscopic mechanisms are investigated to explain this trend. It is further shown that the increasing negativity significantly affects microscopic interlaminar stress distributions.

On crystal shear, lattice rotation and constraint stress in (1 1 0) channel die compression: rate-independent and viscoplastic analyses and predictions compared

Rate-independent crystal plasticity theory and a classic viscoplastic power-law are investigated, contrasted and compared for finite deformation analysis of fcc crystals in channel die compression, including full consideration of lattice straining. Both experiment-based anisotropic and isotropic (Taylor) hardenings are evaluated in rate-independent theory; and an unlimited range of power-law exponent n is considered in viscoplasticity. The focus is on predictions of lateral constraint stress, lattice rotation and crystal shear, and their comparison with experiment. General elastic-plastic equations (for both theories) are given for the range of unstable lattice orientations in (1 1 0) compression (‘range I’) and evaluated before and after a finite rotation of the lattice about the load axis. Equations also are given and evaluated for the ‘Brass’ orientation. It is shown that the theories can be in close agreement at the onset of finite deformation in range I, but that viscoplasticity gives results (for any n) after finite rotation that are in sharp contrast to rate-independent theory. The latter’s predictions for crystal shear and lattice rotation are in good to very good agreement with finite deformation experiments on aluminium and copper. The inclusion of lattice elasticity is found to have a negligible effect in range I. In contrast, for finite deformation in the stable Brass orientation, elastic-viscoplastic theory can be made to agree very closely with rate-independent theory and with experiment.

Numerical stability of non-local viscoplastic FEM analyses for the study of localisation processes

As is well known, numerically handling, by means of finite element codes, localisation problems involving softening materials is still quite delicate. As soon as strain localisation occurs, mesh dependence and serious problems of convergence take place. This paper deals with this type of problem in the case where localisation occurs in an ideal naturally cemented granular specimen tested under plane strain conditions. Different versions (a local elasto-plastic, a local viscoplastic and a non-local viscoplastic) of the same strain softening model are taken into consideration and the relative numerical results are critically discussed and compared. The snap-back problem is numerically taken into account and it has been demonstrated to be affected not only by the softening parameters but also by the viscous nucleus definition. To highlight the relationship between viscosity and non-locality, the results of a numerical parametric analysis are finally discussed.

Viscoplastic analysis of cyclic indentation behavior of thin metallic films

The indentation behavior of metallic thin film is studied numerically, with attention devoted to cyclic response under a fixed load amplitude. The finite element model consists of an aluminum (Al) film above a silicon (Si) substrate, subject to indentation by a diamond indenter. The rate-dependent viscoplastic model of Al is employed. It is shown that, toward the end of the reloading phase of each cycle, plastic deformation continues to occur and the indenter moves deeper into the material. The advancing rate decreases with time, leading to a stabilized response after about ten cycles, in agreement with experimental measurement. Tracking of local deformation history is carried out, to corroborate with the macroscopic indentation response obtained from modeling and experiment.

The Compactions of Elasto-Plastic and Visco-Plastic Granular Assemblies

In this paper, the compactions of the elasto-plastic and the visco-plastic granular assemblies are simulated using the finite element method. Governing equations for motion and deformation for particles, including coupling of rigid body motion and deformation for deformable bodies, are investigated. An implicit discrete element method for block systems is developed to make visco-plastic analysis for the assemblies. Among particles, three different contact types, cohering, rubbing and sliding, are taken into account. To verify accuracy and efficiency of the numerical method, some numerical example is simulated and the results are in a satisfactory agreement with the solutions in literatures. The effects of frictional condition, the initial solid volume ratio, the number of particles in the assembly, and different types of compact- tion on the compaction of the elasto-plastic and the visco-plastic aggregates are investigated. It is demonstrated that the effect of frictional condition, the initial solid volume ratio, the number of particles in the assembly, and different types of compaction on the global behavior of the elasto-plastic the visco-plastic granular assemblies under compacting are considerable. The numerical model is extended to simulate the compaction of aggregates consisting of mixed particles of different viscous incompressible materials. It is indicated that, with minor modification, the method could be used in a variety of problems that can be represented using granular media, such as asphalt, polymers, aluminum, snow, food product, etc.

Viscoplastic analysis for direct impact of sports balls

A coefficient of restitution (COR) is used to represent viscoplastic dissipation of energy in the contact region of colliding bodies [6]. A model has been developed that distinguishes between rate-independent plastic and rate-dependent viscous energy dissipation during impact. A nondimensional contact force shape factor for compression α is introduced which can be measured experimentally. The measured α and COR are used to separate the energy dissipated during collision into part due to plastic deformation and another part due to viscous dissipation. In comparison to the viscoelastic compliance model, the viscoplastic compliance model approximates the force profile accurately, especially in terms of the maximum force that occurs during impact.

Viscoplastic Analysis of Mixed Polygonal Granular Material

In this paper, a series of mixed visco-plastic analyses for assembles of three types of asphalt are made using finite element method. Governing equations are derived for motion and deformation for particles, including coupling of rigid body motion and deformation for deformable bodies. Nonlinear viscous analysis is made for the assemblies using an implicit discrete element method. Among particles, three different contact types, cohering, rubbing and sliding, are taken into account. The numerical model is applied to simulate the compaction of aggregates consisting of mixed particles of different nonlinear viscous incompressible material. After minor modification, the application of the proposed numerical model to industry is possible.

Viscoplastic Analysis of Mixed Polygonal Granular Material

In this paper, a series of mixed visco-plastic analyses for assembles of three types of asphalt are made using finite element method. Governing equations are derived for motion and deformation for particles, including coupling of rigid body motion and deformation for deformable bodies. Nonlinear viscous analysis is made for the assemblies using an implicit discrete element method. Among particles, three different contact types, cohering, rubbing and sliding, are taken into account. The numerical model is applied to simulate the compaction of aggregates consisting of mixed particles of different nonlinear viscous incompressible material. After minor modification, the application of the proposed numerical model to industry is possible.