Academic literature on the topic 'Thermo-viscoplastic Damage Model'

Due to the coefficient of thermal expansion (CTE) mismatch between the bonded layers, the solder joint experiences cycling shear strain, which leads to short cycle fatigue. When semiconductor devices are used in a vibrating environment, additional strains shorten the fatigue life of a solder joint. Reliability of these joints in new packages is determined by laboratory tests. In order to use the FEM to replace these expensive reliability tests a unified constitutive model for Pb40/Sn60 solder joints has been developed and implemented in a thermo-viscoplastic-dynamic finite element procedure. The model incorporates thermal-elastic-viscoplastic and damage capabilities in a unified manner. The constitutive model has been verified extensively against laboratory test data. The finite element procedure was used for coupled thermo-viscoplastic-dynamic analyses for fatigue life predictions. The results indicate that using Miner’s rule to calculate accumulative damage by means of two separate analyses, namely dynamic and thermo-mechanical, significantly underestimates the accumulative total damage. It is also shown that a simultaneous application of thermal and dynamic loads significantly shortens the fatigue life of the solder joint. In the microelectronic packaging industry it is common practice to ignore the contribution of vibrations to short cycle fatigue life predictions. The results of this study indicate that damage induced in the solder joints by vibrations have to be included in fatigue life predictions to accurately estimate their reliability.

We consider a quasistatic frictional contact problem between an elastic-viscoplastic body and an obstacle. The contact is modelled with normal damped response and a local friction law. The material is elastic-viscoplastic with two internal variables which may describe a temperature parameter and the damage of the contacting surface. We provide a variational formulation of the problem and prove the existence of a unique weak solution to the model. The proof is based on arguments of evolution equations with monotone operators, a classical existence and uniqueness result on parabolic inequalities and fixed point.

In this paper, a semi-implicit time integration scheme has been developed for a damage-coupled constitutive model to characterize the mechanical behavior of 63Sn-37Pb solder material under thermo-mechanical fatigue (TMF) loading. The scheme is developed to provide an efficient numerical procedure of integration and iteration for calculating stress and other associated state variables within a strain-driven format. In particular, a novel Newton-Raphson iteration algorithm for the damage coupled constitutive material model involving von Mises viscoplastic potential function with nonlinear mixed hardening is formulated. An algorithmic tangent stiffness tensor is derived and the model is implemented numerically into a commercial finite element (FE) code ABAQUS through its user-defined material subroutine. Several numerical simulations are conducted for validation of the proposed algorithm.

Adiabatic shearing is a typical response of materials under high strain rate loading. Based on the instability analysis for the thermo-viscoplastic constitutive model, a new rate-dependent failure criterion is proposed, where the failure strain decreases with the increment in strain rate. Using the finite element simulation of the Mode-II impact problem for the titanium alloy Ti-6Al-4V, we verified the damage mechanism induced by adiabatic shear band (ASB) under this rate-dependent failure criterion. Also the ASB propagation path and the width of localized shear band are predicted, which is in a good agreement with experimental observation.

The research was based on data obtained from experimental studies and aims in thechallenge of mapping these results by a mathematical (phenomenological) model. The fieldexperiments were performed on an H-section steel column supported by a reinforced concretefoundation and subjected to a close-in explosion. Numerical studies were carried out usingAbaqus/Explicit code. The user subroutine VUMAT for metallic obstacle was also implemented,together with a coupled Eulerian–Lagrangian approach. The steel column failure recorded duringreal field tests versus computational results was examined and compared. It was crucial that, fromthe computational point of view, the obstacle reflected the generalized thermo-elasto-viscoplastic(GTEV) behavior of Perzyna’s type, including an anisotropic measure of damage.

Adiabatic shear band (ASB) is a typical response of materials under high strain rate loading. Based on the instability analysis of the thermo-viscoplastic constitutive model, a new rate-dependent failure criteria is proposed, which links dynamical evolution of ASB with macro mechanical critical conditions, and is successfully applied to account for the shear fracture mode of cylindrical structures subjected to explosive loading. Using finite element method, the transient failure procedure and shearing fragments induced by ASB is simulated, and the calculated fracture profile shows a good agreement with the experimental results. The failure analysis indicates that the rate-dependent failure criteria, as well as impulsive loading, govern the shear damage mode of the structures.

Modelling highly non-linear, strongly temperature- and rate-dependent visco-plastic behaviour of poly-crystalline solids (e.g., metals and metallic alloys) is one of the most challenging topics of contemporary research interest, mainly owing to the increasing use of metallic structures in engineering applications. Numerous classical models have been developed to model the visco-plastic behaviour of poly-crystalline solids. However, limitations of classical visco-plasticity models have been realized mainly in two cases: in problems at the scale of mesoscopic length (typically in the range of a tenth of a micron to a few tens of micron) or lower, and in impact problems under high-strain loading with varying temperature. As a remedy of the first case, several length scale dependent non-local visco-plasticity models have been developed in the last few decades. Unfortunately, a rationally grounded continuum model with the capability of reproducing visco-plastic response in accord with the experimental observations under high strain-rates and varying temperatures remains elusive and attempts in this direction are often mired in controversies. With the understanding of metal visco-plasticity as a macroscopic manifestation of the underlying dislocation motion, there are attempts to develop phenomenological as well as physics-based continuum models that could be applied across different regimes of temperature and strain rate. Yet, none of these continuum visco-plasticity models accurately capture the experimentally observed oscillations in the stress-strain response of metals (e.g. molybdenum, tantalum etc.) under high strain rates and such phenomena are sometimes even dismissed as mere experimental artefacts. The question arises as to whether the existing models have consistently overlooked any important mechanism related to dislocation motion which could be very important at high strain-rate loading and possibly responsible for oscillations in the stress-strain response. In the search for an answer to this question, one observes that the existing macro-scale continuum visco-plasticity models do not account for the effects of dislocation inertia which is identified in this thesis as a dominating factor in the visco-plastic response under high strain rates. Incorporating the effect of dislocation inertia in the continuum response, a visco-plasticity model is developed. Here the ow rule is derived based on an additional balance law, the micro-force balance, for the forces arising from (and maintaining) the plastic flow. The micro-force balance together with the classical momentum balance equations thus describes the visco-plastic response of isotropic poly-crystalline materials. The model is thermodynamically consistent as the constitutive relations for the fluxes are determined on satisfying the laws of thermodynamics. The model includes consistent derivation of temperature evolution, thus replaces the empirical route. Partial differential equations (PDEs) describing the visco-plastic behaviour in the present model is highly non-linear and solving them requires the employment of numerical techniques. Had the interest been limited only to problems with nicely behaved continuous field variables, the finite element method (FEM) could have been a natural choice for solving the governing PDEs. Keeping in mind the limitations of the FEM in discretizing such large deformation problems and in handling discontinuities, a smooth particle hydrodynamics (SPH) formulation for the micro-inertia driven visco-plasticity model is undertaken in this thesis. The visco-plasticity model is then exploited to simulate ductile damage by suitably coupling the discretized SPH equations with an existing damage model. The current scheme does not necessitate the introduction of a yield or damage surface in evolving the plastic strain/ damage parameters and thus the numerical implementation avoids a computationally intensive return mapping. Our current approach therefore provides for an efficient numerical route to simulating impact dynamics problems. However, implementation of the SPH equations demands some additional terms such as artificial viscosity to arrive at a numerically stable solution. Using such stabilizing terms is however bereft of a rational or physical basis. The choice of artificial viscosity parameters is ad-hoc -an inappropriate choice leading to unphysical solutions. In order to circumvent this, the micro-inertia driven visco-plasticity model is reformulated using peri dynamics (PD), a more efficacious scheme to treat shock waves/discontinuities within a continuum model. Remarkably, the PD model naturally accounts for the localization residual terms in the local balances for internal energy and entropy, originally conceived of by Edelen and co-workers nearly half a century ago as a source of non-local interaction. Exploiting the present model, we also explore the determination of conservation laws based on a variational formulation for dissipative visco-plastic solids wherein the system variables are appropriately augmented with those describing the time-reversed dynamics. This in turn enables us to undertake symmetry analyses on the resulting Lagrangian to assess, for instance, material resistance to crack propagation. Specifically, our results confirm that materials with higher rate sensitivity tend to offer higher resistance to fracture. Moreover, it is found that the kinetic energy of the inertial forces contributes to increased plastic flow thereby reducing the available free energy for crack propagation. This part of the work potentially opens a model-based route to the design of micro-defect structures for optimal fracture resistance.

A multiphysics Internal State Variable (ISV) theory that couples the thermoelastoviscoplastic damage model of Bammann-Horstemeyer with electricity-related electromagnetic phenomena is presented in which the kinematics, thermodynamics, and kinetics are internally consistent. An extended multiplicative decomposition of the deformation gradient that accounts for elasticity, plasticity, damage, thermal expansion, electricity, and magnetism is introduced. The different geometrically-affected rate equations are given for each phenomenon after the ISV formalism and have a thermodynamic force pair that acts as an internal stress-like quantity. Guidelines for practical implementation, recommendations for simplifying assumptions, and suggestions for future work supplement the theoretical model. The abstraction of the model can capture the full multi-physics described above; however, the robustness of the model is realized when any of the listed phenomena are not included in the boundary value problem, the model reduces to the previous form — the model will revert to the Bammann-Horstemeyer plasticity-damage ISV model.

A thermo mechanical fatigue life prediction model based on the theory of damage mechanics is presented. The damage evolution, corresponding to the material degradation under cyclic thermo mechanical loading, is quantified thermodynamic framework. The damage, as an internal state variable, is coupled with unified viscoplastic constitutive model to characterize the response of solder alloys. The damage-coupled viscoplastic model with kinematic and isotropic hardening is implemented in ABAQUS finite element package to simulate the cyclic softening behavior of solder joints. Several computational simulations of uniaxial monotonic tensile and cyclic shear tests are conducted to validate the model with experimental results. The behavior of an actual Ball Grid Array (BGA) package under thermal fatigue loading is also simulated and compared with experimental results.

During dynamic loading processes, large inelastic deformation associated with high strain rates leads, for a broad class of ductile metals, to degradation and failure by strain localization. However, as soon as material failure dominates a deformation process, the material increasingly displays strain softening and the finite element computations are considerably affected by the mesh size and alignment. This gives rise to a non-physical description of the localized regions. This paper presents theoretical and computational frameworks to solve this problem with the aid of nonlocal gradient-enhanced theory coupled to visco-inelasticity. Constitutive equations for anisotropic thermo-viscodamage (rate-dependent damage) mechanism coupled with thermo-hypoelasto-viscoplastic deformation are developed in this work within the framework of thermodynamic laws, nonlinear continuum mechanics, and nonlocal continua. Explicit and implicit micro-structural length scale measures, which preserve the well-posedness of the differential equations, are introduced through the use of the viscosity and gradient localization limiters.

Abstract This paper presents a micro-mechanistic approach for modeling fatigue damage initiation due to cyclic creep in eutectic Pb-Sn solder. Damage mechanics due to cyclic creep is modeled with void nucleation, void growth and void coalescence model based on micro-structural stress fields. Micro-structural stress states are estimated under viscoplastic phenomena like grain boundary sliding and its blocking at 2nd phase particles, and diffusional creep relaxation. A conceptual framework is provided to quantify the creep-fatigue damage due to thermo-mechanical cycling. Some parametric studies are provided to better illustrate the utility of the developed model.

The effective use of existing Finite Element Codes in the direct simulation of hypervelocity impacts by projectiles is limited by the dependence of the size of localized failure regions on the mesh size and alignment. This gives rise to a non-physical description of the penetration and perforation processes. A micromechanical constitutive model that couples the anisotropic thermo-viscodamage mechanism with the thermo-hypoelasto-viscoplastic deformation will be presented as a remedy to this situation. Explicit and implicit microstructural length scale measures, which preserve the well-posed nature of the differential equations, are introduced through the use of the viscosity and gradient localization limiters. Simple and robust numerical algorithms for the integration of the constitutive equations will be also presented. The proposed unified integration algorithms are extensions of the classical rate-independent return mapping algorithms to the rate-dependent problems. A simple and direct computational algorithm is also used for implementing the gradient-dependent equations. This algorithm can be implemented in the existing finite element codes without numerous modifications as compared to the current numerical approaches for integrating gradient-dependent models. Model capabilities are preliminarily illustrated for the dynamic localization of inelastic flow in adiabatic shear bands and the perforation of Weldox 460E steel plates with various thicknesses by a deformable blunt projectile at various high impact speeds.

Researchers resort to a wide range of simplified representations at the continuum scale, to model creep-fatigue damage in viscoplastic heterogeneous materials such as Sn-Pb eutectic solders, caused by thermo-mechanical and mechanical cyclic loading (e.g. due to power cycling, environmental temperature cycling, vibration, etc). Typically, in macroscale phenomenological damage models, the cyclic damage is assumed to depend on some loading parameter such as cyclic strain range, work dissipation per cycle, partitioned strain range, partitioned work dissipation per cycle, cyclic entropy changes, cyclic stress range, integrated matrix creep, etc. In many instances, some of these variables are weighted with a factor to account for rate-dependent effects. The task of finding the best damage metric is difficult because of complex microstructural interactions between cyclic creep and cyclic plasticity due to the high homologous temperature under operating conditions. In this study we use insights obtained from microstructural and more mechanistic modeling to identify the most appropriate macro-scale damage metrics. The microstructural models are based on such phenomena as grain boundary sliding, blocking of grain boundary sliding by second-phase particles, grain boundary, volumetric and surface diffusion, void nucleation, void growth and plastic collapse of cavitating grain boundaries. As has been demonstrated in the literature, microstructural models suggest that fatigue damage caused by cyclic plasticity should correlate well with the two most commonly used damage indicators: both cyclic strain range and plastic work dissipation per cycle. This study, however, demonstrates that in the case of damage dominated by cyclic creep, microstructural models developed by the authors indicate closer correlation with creep work dissipation per cycle, than with cyclic creep strain range.

Components of conventional power plants are subject to three potential damage mechanisms and their combination (accumulation) with impact on lifetime considerations: creep, fatigue and ratcheting. Currently, there is a growing need for advanced material models which are able to simulate these damage phenomena and can be implemented effectively within finite-element (FE) codes. This constitutes the basis of an advanced component design. In this work, a constitutive material model, named as the modified Becker-Hackenberg model, is proposed to simulate the thermo-mechanical behavior of high-Cr steel components subject to complex loading conditions. Both creep and viscoplasticity are taken into account in the model, which are viewed as two different kinds of inelastic mechanisms. The key features of the creep strain, i.e., the minimum creep rate and the average creep rupture time, are evaluated by using two Larson-Miller parameters. The cyclic viscoplastic strain is predicted through the conventional Chaboche-type modeling approach, where suitable constitutive evolution equations are adopted to capture the cyclic softening effect, ratcheting effect, time recovery effect and temperature rate effect. All the material parameters involved in this model are identified by using a strategy of stress-range separation. This constitutive model is further implemented in a commercial FE software to simulate the thermo-mechanical behaviors of high-Cr steel components with technologically relevant dimensions. The strain and stress evolution data obtained from the model can be further used for the fatigue damage assessment of high-Cr steel components subject to creep-fatigue interactions. Within an ongoing work, a multiaxial fatigue analyzer is developed to predict the fatigue lifetime of high-Cr steels subject to cyclic loading conditions respectively — in a further step — creep-fatigue interaction.

The salt bath experiment was chosen because of the load characteristics. It is simple enough to allow treatment at moderate cost while containing a geometrical concentration of stress subject to cyclic loading under displacement control (equivalent to thermal control) and leading to a typical situation of creep and localized plasticity with realistic levels of stress and temperature. The specimen (see 1) employed is known as a ‘Type 2 Salt-Bath Specimen’. It is an ax symmetric hollow piece of Type 316 stainless steel as shown in the illustration. The righthand side, in particular the region around the 5 mm radius curve, represents a typical geometrical feature of a tube-tubeplate junction. The left hand-side is a removable plug, allowing periodic inspection of the interior surface, and it is not of structural significance. Specimens are subjected to a purely thermal loading cycle. The cycle is attained by automatically moving specimens back and forth between two baths of a molten salt, at 250 and 600 °C. The total cycle time of the cycle is 16 hours. Viscoplastic constitutive equations with two back-stress variables were used to model the non-isothermal elastic-plastic material behavior. The model parameters were adjusted to tensile, creep and cyclic data for temperatures between 200 and 600 °C. The behavior of the salt bath specimen was calculated with the finite-element program ABAQUS using the UMAT-interface. Two initial states were considered: new material and fully hardened material. For the state ‘new material’ 100 cycles were calculated in order to investigate the local cyclic hardening of the specimen. For the prediction of the lifetime under thermo-mechanical fatigue conditions a damage parameter for TMF-conditions (DTMF) was used. This parameter was calibrated to lifetime data of a similar austenitic material. The location of crack initiation and the number of cycles until crack initiation corresponds reasonably well to the experimental findings.

<div class="section abstract"><div class="htmlview paragraph">Turbocharger housings in internal combustion engines are subjected to severe mechanical and thermal cyclic loads throughout their life-time or during engine testing. The combination of thermal transients and mechanical load cycling results in a complex evolution of damage, leading to thermo-mechanical fatigue (TMF) of the material. For the computational TMF life assessment of high temperature components, the D_TMF model can provide reliable TMF life predictions. The model is based on a short fatigue crack growth law and uses local finite-element (FE) results to predict the number of cycles to failure for a technical crack. In engine applications, it is nowadays often acceptable to have short cracks as long as they do not propagate and cause loss of function of the component. Thus, it is necessary to predict not only potential crack locations and the corresponding number of cycles for a technical crack, but also to determine subsequent crack growth or even a possible crack arrest. In this work, a method is proposed that allows the simulation of TMF crack growth in high temperature components using FE simulations and non-linear fracture mechanics (NLFM).</div><div class="htmlview paragraph">A NLFM based crack growth simulation method is described. This method starts with the FE analysis of a component. In this paper, the method is demonstrated for an automotive turbocharger housing subjected to TMF loading. A transient elastic-viscoplastic FE analysis is used to simulate four heating and cooling cycles of an engine test. The stresses, inelastic strains, and temperature histories from the FEA are then used to perform TMF life predictions using the standard D_TMF model. The crack position and the crack plane of critical hotspots are then identified. Simulated cracks are inserted at the hotspots. For the model demonstrated, cracks were inserted at two hotspot locations. The Δ<i>J</i> integral is computed as a fracture mechanics parameter at each point along the crack-front, and the crack extension of each point is then evaluated, allowing the crack to grow iteratively. The paper concludes with a comparison of the crack growth curves for both hotspots with experimental results.</div></div>

<div class="section abstract"><div class="htmlview paragraph">Semi-Permanent Mold (SPM) cast aluminum alloy cylinder heads are commonly used in gasoline and diesel internal combustion engines. The cast aluminum cylinder heads must withstand severe cyclic mechanical and thermal loads throughout their lifetime. The casting process is inherently prone to introducing casting defects and microstructural heterogeneity. Porosity, which is one of the most dominant volumetric defects in such castings, has a significant detrimental effect on the fatigue life of these components since it acts as a crack initiation site. A reliable analytical model for Thermo-Mechanical Fatigue (TMF) life prediction must take into account the presence of these defects. In previous publications, it has been shown that the mechanism-based TMF damage model (DTMF) is able to predict with good accuracy crack locations and the number of cycles to propagate an initial defect into a critical crack size in aluminum cylinder heads considering ageing effects. In the current work, the model has been extended to also include the effect of porosity which is treated as the initial defect size. It is shown that the model can explain the difference in the fatigue lives of Low-Cycle Fatigue (LCF) samples taken from chilled and non-chilled regions of the heads made of an A356-T6 alloy and tested at different temperatures. On the component level, a non-linear transient elasto-viscoplastic finite element analysis is performed to simulate the thermal cycle that the cylinder head experiences during engine testing including ageing effects. A casting simulation of the head is carried out to provide pore size distribution throughout the casting. The pore sizes are then treated as the initial crack sizes at each node in the mechanism-based short-crack growth model. The TMF life prediction results are compared with zone-based analysis and with engine dyno tests.</div></div>