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The finite element method was used to simulate the thermo-mechanical behaviour of a solder bump configuration on Al2O3 substrate under thermo-cyclic loading between -55 °C and 125 °C. Chaboche's viscoplastic material model was used to describe the Bauschinger effect and the creep/plasticity interaction for the tin-lead solder material. The influence of two different viscoelastic underfill materials (Epoxy+50 % SiO2, Epoxy+70 % SiO2) on the inelastic deformation of the tin-lead solder was analyzed and compared. It may be shown that the thermally matched 'hard' underfiller (Epoxy+70 % SiO2) significantly reduces the accumulated inelastic strain in the bump compared to 'soft' underfiller or no underfill material. On the other hand, the maximum lateral normal stress will increase slightly.
The successive fatigue failure process, i.e. crack initiation and growth up to electrical failure, has been investigated for a flip chip configuration. A cracked and uncracked solder bump was analysed using an unified viscoplastic constitutive model (Chaboche). The electrical failure of a bump seems to be reached in general not before a deep crack has grown into the bump. In order to update the actual loading situation two different cracked structures were calculated.
The finite element method was used to simulate the thermo-mechanical behaviour of a flip chip under thermocyclic loading between -55°C (-67°F) and 125°C (257°F). In order to simulate realistically the inelastic material response of the solder bump, Chaboche's viscoplastic material model instead of a classical ORNL-theory was implemented into the finite element code ABAQUS and applied to a flip chip configuration. This so-called unified constitutive model is able to describe the Bauschinger effect as well as the creep/plasticity interaction. Herewith the influence of the substrate material on the inelastic deformation behaviour of a tin-lead solder bump was analysed. A comparison is given with respect to the influence of the two substrate materials namely Al<sub>2</sub>O<sub>3 </sub> and our self-developed Low Temperature Co-fired Ceramics (LTCC) on the inelastic response of the Sn60Pb40 eutectic solder material. It may be shown that the thermoelastic behaviour of the LTCC substrate significantly reduces the cyclic stresses in the bump compared to Al<sub>2</sub>O<sub>3</sub> as well as the cumulative inelastic strain which is responsible for the development of damage and hence flip chip failure
A general concept for the consideration of the influence of strain gradients on elasto-viscoplastic material behaviour at finite deformation is presented that does not need to account for an additional flow rule for the plastic strain gradient. The balance of momentum including the representation of the stresses, the power of work at contact for the formulation of boundary conditions as well as the nonlocal form of the total power of deformation are derived via the dissipation inequality for the investigated nonpolar continuum model of second grade. In addition to the gradient of the elastic strain tensor, energy storage with gradients of different internal variables is considered: gradient of (i) the plastic strain Tensor itself, (ii) an internal strain tensor induced by viscoplastic straining, by which energy due to hardening is stored also with ist gradient, and (iii) scalar internal variables like the accumulated viscoplastic strain or an internal time variable of damage. Finally, for the simulation of the damage behaviour during a strain hold-time period at a crack tip the responses of a ratedependent and a quasi-rate-independent gradient-enhanced damage model are compared in finite element studies.
During hot extrusion of copper alloys, extrusion tools have to withstand cyclic thermal and mechanical loads. To enhance the service life of the tools, materials with high temperature strength are designed as well as an optimised process control is performed. To characterise the tool damage evolution during service and to improve process guiding, modelling and simulation are appropriate means. The extrusion process of copper billets at three different temperatures was simulated by an FE-program to obtain the temporal boundary conditions, i.e. stress and temperature distributions at the interface billet-liner. Those boundary conditions were used to simulate the elastic–viscoplastic behaviour of the tool steel Böhler W750 in service by means of Abaqus Standard v.6.8-3 software in conjunction with Z-Mat package. A lifetime rule was added in order to compute the lifetime consumption and the cycles to failure.
The uniaxial, torsional and axial-torsional thermomechanical fatigue (TMF) behavior of the near-γ TiAl-alloy TNB-V5 was investigated. TMF tests were performed at 400-800 °C with mechanical strain amplitudes ranging from 0.15% to 0.7%. The tests were conducted thermomechanically in-phase (IP) and out-of-phase (OP).
For the same lifetimes, uniaxial IP tests required the highest strain amplitudes, while OP test conditions were most damaging and needed the lowest strain amplitudes. The Mises equivalent mechanical strain amplitudes of pure torsional tests were found in between uniaxial in-phase and out-of-phase tests for the same lifetimes. The non-proportional multiaxial out-of-phase test showed a lower lifetime at the same equivalent mechanical strain amplitude compared to the other types of tests.
The microstructure has been characterized applying electron microscopy and microstructural parameters such as fraction of twinned grains, grain size, lamellar distance and dislocation density have been quantified.
A material family to replace the current superalloys in aeronautical gas turbine engines is
considered to be that of gamma Titanium Aluminide (γ-TiAl) alloys. Structural components in
aeronautical gas turbine engines typically experience large variations in temperatures and multiaxial
states of stress under non-isothermal conditions. The uniaxial, torsional and bi-axial thermomechanical
fatigue (TMF) behaviour of this γ-TiAl alloy have been examined at 400 800°C with
strain amplitudes from 0.15% to 0.7%. The tests were conducted at both in-phase (IP) and out-ofphase
(OP). The effects of TMF on the microstructure were also investigated. For the same
equivalent mechanical strain amplitude uniaxial IP tests showed significantly longer lifetimes than
pure torsional TMF tests. The non-proportional multiaxial OP test showed the lowest lifetimes at
the same equivalent mechanical strain amplitude compared to the other types of tests.
During aluminium extrusion, the die experience cyclic thermo-mechanical loads that can lead to materials degradation and failure. For a process optimization and a comparison of different hot work tool steels, the finite element method is an appropriate means. Local inelastic strains result from the interaction of the applied temperature and stress loading and can be computed by suitable inelastic constitutive equations. Stress amplitudes and dwell times during extrusion result in creep-fatigue damage. A lifetime consumption model sums increments of a damage variable over time and defines materials failure as the accumulation of the resulting damage variable to a critical value. The procedure for the identification of the material parameters for both the constitutive and the damage model is described in detail, including the material parameters for the description of time-effects, and applied to the hot work tool steel Böhler W300 ISOBLOC (EN 1.2343). The lifetime consumption for two different hot work tool steels is compared on the basis of an example in aluminium extrusion.
During hot extrusion of aluminium alloys, extrusion dies experience cyclic temperature changes as well as multiaxial loadings. To improve the service life of the dies, cleaner and high hot strength materials are designed as well as an optimised process control is performed. For the improvement of the process guiding and a comparison of lifetime behaviour of different hot work tool steels, modelling and simulation are appropriate means. The extrusion process has been simulated using the FE-program Deform to find the stress and temperature history at the inner diameter of the liner, i.e. the boundary conditions for the subsequent cyclic simulation of the container during service. Inelastic constitutive equations have been implemented into Abaqus Standard to describe strain hardening and time recovery effects. They include the Norton viscoplastic flow rule, thermo-mechanical isotropic hardening and two non-linear kinematic hardening laws. A damage-rate model predicts failure and thus the lifetime of the container. The procedure for the identification of material parameters for both the constitutive and the damage model is described in detail for the hot work tool steel Böhler W400 VMR (EN 1.2343).
Für viskoplastische Stoffgesetze wird das prinzipielle Verfahren der Identifikation von Materialmodell-Parametern für das Spannungs-Verformungs- und Versagens-Verhalten metallischer Werkstoffe am Beispiel von Hochtemperatur-Ermüdung aufgezeigt. Dies betrifft zum Einen die Verwendung geeigneter und auch möglichst weniger Experimente zur Hervorbringung der zu beschreibenden Phänomene des Werkstoffverhaltens und deren gezielte Auswertung sowie zum Anderen die physikalisch kontrollierte Führung einer numerischen Optimierung zur Ermittlung vertrauenswürdiger Materialparameterwerte. Diese Vorgehensweise wurde erfolgreich auf Warmarbeitsstähle sowie poly- und einkristalline Superlegierungen angewendet.
A hierarchy of higher order continua is presented that introduces additional degrees of freedom accounting for volume changes, rotation and straining of an underlying microstructure. An increase in the number of degrees of freedom represents a refinement of the material description. In addition to available nonlinear Cosserat and micromorphic theories, general formulations of elastoviscoplastic behaviour are proposed for microdilatation and microstretch continua. A microstrain theory is introduced that is based on six additional degrees of freedom describing the pure straining of the microstructural element. In each case, balance equations and boundary conditions are derived, decompositions of the finite strain measures into elastic and plastic parts are provided. The formulation of finite deformation elastoviscoplastic constitutive equations relies on the introduction of the free energy and dissipation potentials, thus complying with requirements of continuum thermodynamics. Some guidelines for the selection of a suitable higher order model for a given material close the discussion.
This work deals with the formulation of a three-dimensional crystallographic time-incremental lifetime rule for face-centered cubic (fcc) single crystals used for gas-turbine blade applications. The damage contribution rate of each slip system to the total damage is governed by the current values of the resolved shear stress and the slip rate on the corresponding slip system. The damage rule is combined with a crystallographic viscoplastic deformation model. For the nickel-base single-crystal superalloy CMSX4 at 950 °C, various strain- and stress-controlled uniaxial cyclic tests with and without hold-times can be described for different crystal orientations by one set of material parameters. For verification, simulation results for a single-crystal specimen with a notch have been compared with corresponding experimental results. The predicted lifetime is within the factor of two of the measured one.
Laird and Smith [(1962). Philosophical Magazine 8, 847857] proposed a plastic sliding-off mechanism for the stage II fatigue crack growth via striation formation. In their view, the fatigue crack extension results solely from the changing character of deformation at the crack tip during loading and unloading. In particular, the crack tip blunts during the loading stage and folds into a double notch during the unloading stage, resulting in striation formation. In order to verify Lairds plastic blunting mechanism for ductile polycrystals as well as for ductile fcc single crystals, FE calculations were performed for a rectangular plate with an initially sharp crack under plane strain conditions. The plate was subjected to a fully reversed tension-to-pressure cyclic load perpendicular to the crack plane (Mode 1). In the single crystal case the crack propagation simulations were carried out for cracks with crack plane (001) for two different crack growth orientations [110] and [100]. No initial radius for the crack tip was assumed. The actual shape of the crack tip followed from an initially sharp crack by repeated remeshing. To model the constitutive behavior typical for polycrystalline ductile metals, J2 hypo-elasto-plasticity model with ArmstrongFrederick kinematic hardening was used. To model the constitutive behavior typical for ductile fcc single crystals, a geometrically nonlinear version of Cailletauds model based on the multiplicative elasto-plastic decomposition of the deformation gradient was implemented into the FE program ABAQUS. For simplicity, only octahedral slip systems were considered. Using repeated remeshing for severely distorted elements at the advancing crack tip, deformation patterns in the sense of Lairds mechanism for fatigue crack propagation with striation formation were obtained in the case of the polycrystal simulation as well as in the case of the single crystal simulation for [110] crack growth direction. The simulation for [100] crack growth direction with the same stress level as for [110] direction also yielded crack extension by progressive large deformations but without striation formation. The dependence of the fatigue striation formation on the crack growth direction as predicted by the simulation of crack propagation in single crystals is verified by the experimental results of Neumann [(1974). Acta Metallurgica 22, 11551165] on pure copper single crystals.
In this work, the influence of the development of geometrically necessary dislocations (GNDs) at a crack tip in single crystals on the hardening and crack propagation behaviour is investigated. In particular, we are interested in examining the effect of such additional hardening on the development of glide and kink bands at the crack tip as well as on the process of crack opening. To this end, following Nye and many others, local deformation incompatibility in the material is adopted as a measure of the density of GNDs. Their development results in additional energy being stored in the material, leading to additional kinematic-like hardening. A thermodynamic formulation of the model in the context of the dissipation principle facilitates the derivation of the corresponding hardening relation. Results suggest that this additional hardening retards kink-band development, but has little or no influence on glide-band development. It also influences the crack tip opening displacement (CTOD). It turns out that the simulated CTOD correlates well with experimentally determined crack-propagation rates for different crack growth direction in the crystal.
Weiterentwicklung der Simulation der Span-Segmentierung unter Berücksichtigung duktiler Schädigung
(2003)
A unifying thermomechanical constitutive framework for generalized continua including additional degrees of freedom or/and the second gradient of displacement is presented. Based on the analysis of the dissipation, state laws, flow rules and evolution equations are proposed for Cosserat, strain gradient and micromorphic continua. The case of the gradient of internal variable approach is also incorporated by regarding the nonlocal internal variable as an actual additional degree of freedom. The consistency of the continuum thermodynamical framework is ensured by the introduction of a viscoplastic pseudopotential of dissipation, thus extending the classical class of socalled standard material models to generalized continua.
Variants of the higher order and higher grade theories are also reported based on the explicit introduction of the plastic strain tensor as additional degree of freedom. Within this new class of models, called here gradient of strain models, one recognizes the fact that, in a second grade theory for instance, the plastic part of the strain gradient can be identified with the gradient of plastic strain.
Simple examples dealing with bending and shearing of Cosserat or second grade media are given to illustrate two types of extensions of classical J 2-plasticity : single-criterion and multi-mechanism generalized elastoplasticity.
Finally, formulations at finite deformation of the proposed models are provided focusing on proper decompositions of Cosserat curvature, strain gradient and gradient of micromorphic deformation into elastic and viscoplastic parts.