Full Thermomechanical Coupling Research Articles

Peridynamic analysis of thermomechanical effects in fracture toughening mechanisms of stop holes

In this study, a bond-based fully coupled thermomechanical peridynamic framework is implemented to study the fracture toughening of stop-holes in brittle materials subjected to thermomechanical loads. The developed modelling approach aims to provide comprehensive guidance about thermal effects on the fracture toughening mechanism of inclusions under realistic engineering conditions. First, the model is verified using simulation of several benchmark case studies and predicts the mechanical, thermal and damage parameters with high accuracy. Then, a fully coupled thermomechanical analysis of a 2D structure is performed to study the effect of the location of a single stop-hole on fracture toughening. A thorough investigation of the arresting and accelerating effect of the stop-hole is conducted. Additionally, the accuracy of various degrees of thermomechanical coupling including one-way weak coupling and no coupling is compared with full coupling. The study of crack propagation dynamics reveals that ignoring thermal effects underpredicts the toughness enhancement of stop-holes. Furthermore, although the weak thermomechanical coupling offers a reasonable prediction of crack propagation dynamics in most cases of our study, it is not accurate in certain cases. In the final section, some benchmark cases of complex arrangements of multiple stop-holes in literature are revisited. Our results indicate a different toughness trend for some cases when considering the full thermomechanical coupling. This suggests the proposed framework provides a more accurate tool for designing toughened structures using inclusions.

A Variational Framework for the Thermomechanics of Gradient-Extended Dissipative Solids \u2013 with Applications to Diffusion, Damage and Plasticity

The paper presents a versatile framework for solids which undergo nonisothermal processes with irreversibly changing microstructure at large strains. It outlines rate-type and incremental variational principles for the full thermomechanical coupling in gradient-extended dissipative materials. It is shown that these principles yield as Euler equations essentially the macro- and micro-balances as well as the energy equation. Starting point is the incorporation of the entropy and entropy rate as canonical arguments into constitutive energy and dissipation functions, which additionally depend on the gradient-extended mechanical state and its rate, respectively. By means of (generalized) Legendre transformations, extended variational principles with thermal as well as mechanical driving forces can be constructed. On the thermal side, a rigorous distinction between the quantity conjugate to the entropy and the quantity conjugate to the entropy rate is essential here. Formulations with mechanical driving forces are especially suitable when considering possibly temperature-dependent threshold mechanisms. With regard to variationally consistent incrementations, we suggest an update scheme which renders the exact form of the intrinsic dissipation and is highly suitable when considering adiabatic processes. It is shown that this proposed numerical algorithm has the structure of an operator split. To underline the broad applicability of the proposed framework, we set up three model problems as applications: Cahn-Hilliard diffusion coupled with temperature evolution, where we propose a new variational principle in terms of the species flux vector, as well as thermomechanics of gradient damage and gradient plasticity. In a numerical example we study the formation of a cross shear band.

Global dynamics perspective on macro- to nano-mechanics

In about the last two decades, global nonlinear dynamics has been evolving in a revolutionary way, with the development of sophisticated techniques employing concepts/tools of dynamical systems, bifurcation, and chaos theory, and applications to a wide variety of mechanical/structural systems. The relevant achievements entail a substantial change of perspective in dealing with vibration problems and are ready to meaningfully affect the analysis, control, and design of systems at different scales, in multiphysics contexts too. After properly framing the subject within some main stages of developments of nonlinear dynamics in solid/structural mechanics, as occurred over the last 40 years, the article focuses on highlighting the role played by global analysis in unveiling the nonlinear response and actual safety of engineering systems in different environments. Reduced order models of macro-/micro-structures are considered. Global dynamics of a laminated plate with von Karman nonlinearities, shear deformability, and full thermomechanical coupling allows to highlight the meaningful effects entailed by the slow transient thermal dynamics on the fast steady mechanical responses. An atomic force microcantilever is referred to for highlighting the severe worsening of overall stability associated with the application of an external feedback control and the importance of global dynamics for conceiving and effectively implementing a control procedure aimed at enhancing engineering safety. The last part of the article dwells on the general role that a global dynamics perspective is expected to play in the safe design of real systems, in the near future, focusing on how properly exploiting concepts and tools of dynamical integrity to evaluate response robustness in the presence of unavoidable imperfections, and to improve the system’s actual load carrying capacity.

Full thermomechanical coupling in modelling of micropolar thermoelasticity

The present paper is devoted to plane harmonic waves of displacements and microrotations propagating in fully coupled thermoelastic continua. The analysis is carried out in the framework of linear conventional thermoelastic micropolar continuum model. The reduced energy balance equation and the special form of the Helmholtz free energy are discussed. The constitutive constants providing fully coupling of equations of motion and heat conduction are considered. The dispersion equation is derived and analysed in the form bi-cubic and bi-quadratic polynoms product. The equation are analyzed by the computer algebra system Mathematica. Algebraic forms expressed by complex multivalued square and cubic radicals are obtained for wavenumbers of transverse and longitudinal waves. The exact forms of wavenumbers of a plane harmonic coupled thermoelastic waves are computed.

Continuous chip formation in metal cutting processes using the Particle Finite Element Method (PFEM)

This paper presents a study on the metal cutting simulation with a particular numerical technique, the Particle Finite Element Method (PFEM) with a new modified time integration algorithm and incorporating a contact algorithm capability . The goal is to reproduce the formation of continuous chip in orthogonal machining. The paper tells how metal cutting processes can be modelled with the PFEM and which new tools have been developed to provide the proper capabilities for a successful modelling. The developed method allows for the treatment of large deformations and heat conduction, workpiece-tool contact including friction effects as well as the full thermo-mechanical coupling for contact. The difficulties associated with the distortion of the mesh in areas with high deformation are solved introducing new improvements in the continuous Delaunay triangulation of the particles. The employment of adaptative insertion and removal of particles at every new updated configuration improves the mesh quality allowing for resolution of finer-scale features of the solution. The performance of the method is studied with a set of different two-dimensional tests of orthogonal machining. The examples consider, from the most simple case to the most complex case, different assumptions for the cutting conditions and different material properties. The results have been compared with experimental tests showing a good competitiveness of the PFEM in comparison with other available simulation tools.

Softening behavior of quasi-brittle material under full thermo-mechanical coupling condition: Theoretical formulation and finite element implementation

In this article we introduce a new thermo-damage model, which is capable of modeling the softening behavior of quasi-brittle under loading condition including temperature change. The theoretical formulation and numerical solution procedure to solve the problem in the most general case of full thermo-mechanical coupling are presented.

A thermo-mechanically coupled field model for shape memory alloys

The impressive properties of shape memory alloys are produced by means of solid-to-solid phase transformations where thermal effects play an important role. In this paper, we present a model for polycrystalline shape memory alloys which takes full thermo-mechanical coupling into account. Starting from the equations of the first and the second law of thermodynamics, we derive evolution equations for the volume fractions of the different martensitic variants and a related equation for heat conduction. A thermodynamic analysis allows to formulate a complete expression for the dissipation caused by phase transformation and heat flux. This allows to model the experimentally well-documented transformation fronts in tension tests by a finite element scheme without further assumptions. Additionally, the number of required model parameters is very small in comparison with phenomenological approaches. Numerical examples are presented which show a good agreement with experimental observations.

The analysis of localized effects in composites with periodic microstructure

Several methods for the analysis of composite materials with periodic microstructure in which localized effects (such as concentrated loads, cracks and stationary/progressive damage) occur are resented. Owing to the loss of periodicity caused by these localized effects, it is no longer possible to identify and analyse a repeating unit cell that characterizes the periodic composite. For elastostatic problems, these methods are based on the combination of the representative cell method (RCM), the higher-order theory for functionally graded materials and often the high-fidelity generalized method of cells (HFGMC) micromechanical model. For elastodynamic problems, the combination of the dynamic RCM with a theory for wave propagation in heterogeneous media is used for the prediction of the time-dependent response of the periodic composite with localized effects. In the framework of the RCM, the problem for a periodic composite that is discretized into numerous identical cells is reduced to a problem of a single cell in the discrete Fourier transform domain. In the framework of the higher-order theory and the theory of wave propagation in composites, the resulting governing equations and interfacial conditions in the transform domain are solved by dividing the single cell into subcells and imposing the latter in an average (integral) sense. The HFGMC is often used for the prediction of the proper far-field boundary conditions based on the response of the unperturbed composite. The inverse of the Fourier transform provides the real elastic field at any point of a composite with localized effects. This research summarizes a series of investigations for the prediction of the behaviour of periodic composites with localized loading, fibre loss, damage and cracks subjected to static and dynamic loadings under isothermal and full thermomechanical coupling conditions.

Heating and cooling effects generated by the dynamic stresses of cracked interfaces and layers in laminated composites

The temperature field generated by the sudden application of a far-field mechanical loading of a periodically layered composite with an interfacial crack or with a cracked layer parallel to the interfaces is determined. As a result of the crack’s existence, the periodicities of the structure and the thermoelastic field are lost. The complexity of the resulting problem is resolved by the combined application of the representative cell method and the full (two-way) dynamic thermomechanical equations. In the former analysis, due to the loss of periodicity the dynamic thermoelastic Green’s functions are generated, in conjunction with the double finite discrete Fourier transform. In the latter one, the transformed displacements and temperature are expressed by second-order expansions and the strong-form of the elastodynamic and energy equations together with the various interfacial and the so called Born–von Karman boundary conditions are imposed in the average sense (in the transform domain). The results exhibit the induced temperature field at any point in the plane of the crack. The generated temperature fields show the cooling and heating zones in both Mode I and Mode II deformations. In addition, the adiabatic assumption (according to which the heat conduction is a priori ignored) is assessed by comparing the computed temperature field with the corresponding one based on the full thermomechanical coupling.

A limit analysis approach to derive a thermodynamic damage potential for non-linear geomaterials

This paper introduces a mathematical model which describes the continuum damage of non-linear geo-materials. The model accounts for full thermo-mechanical coupling as well as irreversible failure and its effect on shear heating. It involves multi-mechanisms creep to describe the material rheology depending on time, temperature, pressure and water content. This coupled thermo-mechanical model combined with the upper bound theory is used to formulate a potential capable of predicting the damage evolution. The model is implemented and applied to a cross-sectional geological layer subjected to extension. It reveals that damage accelerates the creation of faults and accentuates the localization of shear zones, thereby competing with the increase in material rigidity due to rate dependency, especially at high temperature.

The temperature field induced by the dynamic stresses of a transverse crack in periodically layered composites

The temperature field induced by the dynamic application of a far-field mechanical loading on a periodically layered material with an embedded transverse crack is investigated. To this end, the thermoelastically coupled elastodynamic and energy (heat) equations are solved by combining two approaches. In the first one, the dynamic representative cell method is employed for the construction of the time-dependent Green’s functions generated by the displacement jumps along the crack line. This is performed in conjunction with the application of the double finite discrete Fourier transform on the thermomechanically coupled equations. Thus the original problem for the cracked periodic composite is reduced to the problem of a domain with a single period in the transform space. The second approach is based on wave propagation analysis in composites where full thermomechanical coupling in the constituents exists. This analysis is based on the coupled elastodynamic-energy continuum equations where the transformed time-dependent displacement vector and temperature are expressed by second-order expansions, and the elastodynamic and energy equations and the various interfacial and boundary conditions are imposed in the average (integral) sense. The time-dependent thermomechanically coupled field at any observation point in the plane can be obtained by the application of the inverse transform. Results along the crack line as well as the full temperature field are given for cracks of various lengths for Mode I and Mode II deformations. In particular the temperature drops (cooling) at the vicinity of the crack’s tip and the heating zones at its surroundings are generated and discussed.

The effect of anisotropic damage evolution on the behavior of ductile and brittle matrix composites

Anisotropic damage evolution laws for ductile and brittle materials have been coupled to a micromechanical model for the prediction of the behavior of composite materials. As a result, it is possible to investigate the effect of anisotropic progressive damage on the macroscopic (global) response and the local spatial field distributions of ductile and brittle matrix composites. Two types of thermoinelastic micromechanics analyses have been employed. In the first one, a one-way thermomechanical coupling in the constituents is considered according to which the thermal field affects the mechanical deformations. In the second one, a full thermomechanical coupling exists such that there is a mutual interaction between the mechanical and thermal fields via the energy equations of the constituents. Results are presented that illustrate the effect of anisotropic progressive damage in the ductile and brittle matrix phases on the composite’s behavior by comparisons with the corresponding isotropic damage law and/or by tracking the components of the damage tensor.

Experimental and Computational Investigation of Machining Processes for Functionally Graded Materials

Experiments on dry face turning of functionally graded heat treatable steel are conducted. The workpieces have a hardened zone of approx. 60 HRC and a non-hardened zone of approx. 30 HRC. PCBN tools are used with different feeds, cutting speeds and depths of cut. Measurements of residual stresses in the surface layer reveal compressive stresses in the hardened zone and tensile stresses in the non-hardened zone. These experimental observations are compared with the results of representative simulations of the cutting process. A large-deformation thermo-elasto-viscoplastic material model is used and the geometry of the cutting tool is precisely reflected by the finite element discretisation. To predict the overall response, an adaptive remeshing scheme and full thermo-mechanical coupling is accounted for. Moreover, measured residual stresses are incorporated as initial conditions within the simulation.

High-speed frictional slip at metal-on-metal interfaces

In this study plate-impact pressure-shear friction experiments are employed to investigate dynamic slip resistance and time-resolved growth of molten metal films during dry metal-on-metal slip under extreme interfacial conditions. By employing a tribo-pair comprising of a hard tool-steel against a relatively low melt-point metal (7075-T6 Al alloy), interfacial normal stress of up to 5 GPa and slip speeds of approximately 250 m/s have been achieved. These extreme interfacial conditions are conducive to the development of molten metal film at the tribo-pair interface. A Lagrangian finite element code is developed to understand the evolution of the thermo-mechanical fields and their relationship to the observed slip response. The code accounts for dynamic effects, heat conduction, contact with friction, and full thermo-mechanical coupling. At temperatures below the melting point of the tribo-pair materials are described as isotropic, thermally softening, elastic–viscoplastic solids. For material elements with temperatures in excess of the melt temperature a purely Newtonian fluid constitutive model is employed. The results of this hybrid experimental–computational approach provide new insights into the thermo-plastic interactions during the high-speed metal-on-metal slip. During the early part of frictional slip the coefficient of kinetic friction is observed to decrease with increasing slip velocity. During the later part, transition in interfacial slip occurs from dry metal-on-metal sliding to the formation of molten Al film at the slip interface. During this slip phase, the interfacial resistance approaches the shear strength of the molten Al alloy under normal pressures of approximately 1–4.5 GPa and shear-strain rates of ∼10 7 s −1. The results of the study indicate that under such extreme interfacial conditions molten aluminum films maintain a shearing resistance as high as 50–100 MPa. Scanning electron microscopy of the slip surfaces reveal molten aluminum to be smeared on the tribo-pair interface at high impact velocities. Also, the extent of the molten area, as observed from the SEM micrographs, increases with increasing impact velocities.

Investigation of shape memory alloy honeycombs by means of a micromechanical analysis

Shape memory alloy (SMA) honeycombs are promising new smart materials which may be used for light-weight structures, biomedical implants, actuators and active structures. In this study, the behavior of several SMA honeycomb structures is investigated by means of a continuum-based thermomechanically coupled micromechanical analysis. To this end, macroscopic inelastic stress–strain responses of several topologies are investigated, both for pseudoelasticity and for shape memory effect. It was found that the triangular topology exhibits the best performance. In addition, the initial transformation surfaces are presented for all possible combinations of applied in-plane stresses. A special two-phase microstructure that is capable of producing an overall negative coefficient of thermal expansion is suggested and studied. In this configuration, in which one of the phases is a SMA, residual strains are being generated upon recovery. Here, the negative coefficient of thermal expansion appears to be associated with a larger amount of residual strain upon recovery. Furthermore, a two-dimensional SMA re-entrant topology that generates a negative in-plane Poisson's ratio is analyzed, and the effect of the full thermomechanical coupling is examined. Finally, the response of a particular three-dimensional microstructure is studied.

Identification of material parameters of a thermo-mechanical model for pebble beds in fusion blankets

In this paper, a thermo-mechanical model of pebble beds is adopted [D. Hofer, M. Kamlah, Drucker-Prager-Cap creep modelling of pebble beds in fusion blankets, Fusion Eng. Des. 73 (2005) 105–117] and developed based on experiments by Dr. Reimann at Forschungszentrum Karlsruhe (FZK). The framework of the present material model is composed of a non-linear elastic law [O. Coube, Modelling and numerical simulation of powder die compaction with consideration of cracking, PhD Thesis, University Pierre et Marie, Paris VI, 1998], the Drucker-Prager-Cap theory [ABAQUS, Analysis User's Manual, Version 6.5, 2004], a modified creep law [D. Hofer, M. Kamlah, Drucker-Prager-Cap creep modelling of pebble beds in fusion blankets, Fusion Eng. Des. 73 (2005) 105–117]. Furthermore, the volumetric inelastic strain dependent thermal conductivity of beryllium pebble beds [J. Reimann, G. Piazza, Z. Xu, A. Goraieb, H. Harsch, Measurements of the thermal conductivity of compressed beryllium pebble beds, FZKA 7096 (2005)] is taken into account and full thermo-mechanical coupling is considered. By analyzing the deformation mechanism of the oedometric experiments, a new method is developed to determine the set of material parameters, including the temperature dependent hardening law. With the new method, the material parameters can be derived directly from the empirical equations (the so-called “Reimann fits” for pebble beds) including the thermoplastic behaviour. All these thermo-mechanical constitutive laws are implemented in ABAQUS by user defined field (USDFLD) and CREEP subroutines. The oedometric compression tests and creep tests under different temperatures are simulated by the present model, and the results show that the model gives a good description of experimental results. The analysis on the precompaction procedure of pebble beds assembly (PBA) is applied to show the feasibility of the present material model.

Thermo-Mechanical Modelling of Pebble Beds in Fusion Blankets and its Implementation by a Return-Mapping Algorithm

AbstractIn this investigation, a thermo-mechanical model of pebble beds is adopted and developed based on experiments by Dr. Reimann at Forschungszentrum Karlsruhe (FZK). The framework of the present material model is composed of a non-linear elastic law, the Drucker-Prager-Cap theory, and a modified creep law. Furthermore, the volumetric inelastic strain dependent thermal conductivity of beryllium pebble beds is taken into account and full thermo-mechanical coupling is considered.Investigation showed that the Drucker-Prager-Cap model implemented in ABAQUS can not fulfill the requirements of both the prediction of large creep strains and the hardening behaviour caused by creep, which are of importance with respect to the application of pebble beds in fusion blankets [1]. Therefore, UMAT (user defined material's mechanical behaviour) and UMATHT (user defined material's thermal behaviour) routines are used to re-implement the present thermo-mechanical model in ABAQUS. An elastic predictor radial return mapping algorithm is used to solve the non-associated plasticity iteratively, and a proper tangent stiffness matrix is obtained for cost-efficiency in the calculation. An explicit creep mechanism is adopted for the prediction of time-dependent behaviour in order to represent large creep strains in high temperature. Finally, the thermo-mechanical interactions are implemented in a UMATHT routine for the coupled analysis.The oedometric compression tests and creep tests of pebble beds at different temperatures are simulated with the help of the present UMAT and UMATHT routines, and the comparison between the simulation and the experiments is made.

Formation of molten metal films during metal-on-metal slip under extreme interfacial conditions

The present paper describes results of plate-impact pressure-shear friction experiments conducted to study time-resolved growth of molten metal films during dry metal-on-metal slip under extreme interfacial conditions. By employing tribo-pairs comprising hard tool-steel against relatively low melt-point metals such as 7075-T6 aluminum alloys, interfacial friction stress ranging from 100 to 400 MPa and slip speeds of approximately 100 m/ s have been generated. These relatively high levels of friction stress combined with high slip-speeds generate conditions conducive for interfacial temperatures to approach the melting point of the lower melt point metal (Al alloy) comprising the tribo-pair. A Lagrangian finite element code is developed to understand the evolution of the thermo-mechanical fields and their relationship to the observed slip response. The code accounts for dynamic effects, heat conduction, contact with friction, and full thermo-mechanical coupling. At temperatures below the melting point the material is described as an isotropic thermally softening elastic-viscoplastic solid. For material elements with temperatures in excess of the melt point a purely Newtonian fluid constitutive model is employed. The results of the hybrid experimental-computational study provides new insights into the thermoelastic–plastic interactions during high speed metal-on-metal slip under extreme interfacial conditions. During the early part of frictional slip the coefficient of kinetic friction is observed to decrease with increasing slip velocity. During the later part transition in interfacial slip occurs from dry metal-on-metal sliding to the formation of molten Al films at the tribo-pair interface. Under these conditions the interfacial resistance approaches the shear strength of the molten aluminum alloy under normal pressures of approximately 1– 3 GPa and shear strain rates of ∼10 7 s −1 . The results of the study indicate that under these extreme conditions molten aluminum films maintain a shearing resistance as high as 100 MPa . Scanning electron microscopy of the slip surfaces reveal molten aluminum to be smeared on the tribo-pair interface. Knoop hardness measurements in 7075-T6 Al alloy at various depths from the slip interface indicate that the hardness increases approximately linearly with depth and reaches a plateau at approximately 40 μm from the surface.

Micromechanical analysis of the fully coupled finite thermoelastic response of rubber-like matrix composites

A micromechanical analysis for the prediction of the coupled thermoelastic response of multiphase composites that include rubber-like phases is presented. Rubber-like solids are highly nonlinear thermoelastic materials that exhibit anomalous behavior referred to as the thermoelastic inversion effect. Results are presented which show that the derived micromechanical model is capable of predicting this effect in nylon/rubber composites subjected to appropriate thermal loadings assuming one-way coupling. For full thermomechanical coupling, the nonlinear response and induced temperatures under several types of mechanical loading are investigated.

A FULLY COUPLED THERMO-MECHANICAL MICROMECHANICS MODEL

The development for a micromechanical model with full thermomechanical coupling, which is based on the combined effects of the mechanical and energy equations, is presented. The model is based on a combined approximate kinematic and thermal analysis of a repeating unit cell in a triply periodic array of inclusions. The unit cell is considered to consist of different subregions that can be composed of any desired material. The behavior of the material within the different subregions can be modeled using elastic, plastic, viscoelastic, viscoplastic, or damage constitutive models. The analysis satisfies the equations of motion and the energy equation for the different subregions of the unit cell in an average sense. The interfacial continuity conditions for the velocities, stresses, temperature, and thermal fluxes between the different subregions are also satisfied in an average sense. Arbitrary heat source terms are included in the energy equation to allow for the analysis of reactive materials. The resulting system of governing equations exhibits full coupling between the deformations and the thermal effects. The proposed model is analytical and provides closed-form expressions for the effective macroscopic kinematic and thermal behavior of a particulate composite. The influence of the thermomechanical coupling on behavior at both the macroscopic and microscopic levels is considered. The presence of the coupling can lead to significant localization of the thermal and deformation responses within different regions of the unit cell. It is shown that the presence of inelastic deformations in conjunction with thermomechanical coupling effects can result in appreciable deviation from an isothermal, inelastic analysis.