Thermomechanical Approach Research Articles

Prediction of cutting forces in 3-axes milling of sculptured surfaces directly from CAM tool path

In the present work a new approach for the modelling of milling is described. The cutting forces are calculated for milling operations directly from the tool path provided by a Computer Assisted Manufacturing program. The main idea consists in using tool position points coming from CAM data in order to calculate the local inclination angle of the generated surface and then the tool engagement in the machined material. A good approximation for global and local cutting forces can be obtained when an analytical model able to predict the cutting forces for 3-axes milling is used. Two approaches are proposed to calculate the local cutting forces to show the versatility of the method. The first method uses a thermomechanical approach using a Johnson & Cook constitutive law while the second is based on classical cutting coefficients. Some results are presented for wavelike form and free form machining tests and are compared with experimental data obtained in roughing and finishing of 42CrMo4 steel. Results are satisfactory and the capability of the method to predict the resultant surface roughness is shown.

A thermomechanical framework for non-linear hyperviscoelastic materials

Visco-elastic models are commonly used in modeling time dependent behavior of asphalts, polymers, and biomaterials (e.g., soft tissues). In order to ensure that these models are thermomechanically consistent, their stress-strain behavior has to be derived using a strain energy function. For a non-linear viscoelastic behavior, this appears to be a rather subtle problem: some quasi-linear viscoelastic energy formulations presented in the literature do not use the true energy functions for the stress-strain response attributed to these models, making their mechanical interpretation and validation of thermomechanical consistency difficult. This paper represents an attempt to propose an alternative framework, which would retain simplicity and convenience in numerical applications of the quasi-linear viscoelasticity, but would have a straightforward mechanical interpretation and guarantee the thermomechanical consistency. This is achieved by using a thermomechanical approach with internal kinematic variables, where both the energy and dissipation potentials have the same kind of non-linearity, leading to a general family of non-linear visco-elastic models. Within this context, a simple thermomechanically consistent non-linear hyperviscoelastic model with pressure dependent bulk stiffness is proposed, with an example modeling experimental data from laboratory tests on asphalts.

Characterisation of power modules ceramic substrates for reliability aspects

Electronic power devices used for transportation applications (automotive and avionics) experience severe temperature variations which promote their thermal fatigue and failure. For example, for power modules mounted on the engine of an aircraft, temperature variations range from −55 °C (in the worst case of storage before takeoff) to +200 °C (flight). In theses conditions failure (conchoïdal fracture) can occur in DBC substrates. The Weibull approach was used to model the brittle fracture of the ceramic layer from a natural defect. Besides, geometric singularities in the upper ceramic/copper interface are at the origin of cracks, which grow by fatigue and finally bifurcate and break the ceramic layer. With the framework of linear elastic fracture mechanics (LEFM) and using the finite element method, it was possible to analyse how a thermal loading history may modify the risk of failure of the DBC substrate and can increase the fatigue life of a power module. This result shows that the fatigue life and the reliability of power electronic devices could be optimized using a thermo-mechanical approach of the problem and suitable failure criteria.

High Temperature Long Period Grating Thermo-Mechanically Written

An optical fiber transducer able to work in high temperature environments is experimentally demonstrated in the laboratory. It is based on a permanent long period grating (LPG) written using a new technique based on a thermo-mechanical approach. Device precision was experimentally checked by means of repetitive thermal cycles between 25 and 950 °C. In addition device stability was assured by maintaining the temperature in steady state at 800 °C during 23 hours.

Thermal fatigue and failure of electronic power device substrates

Electronic power devices used for transportation applications (automotive and avionics) experience severe temperature variations, which promote their thermal fatigue and failure. For example, for power modules mounted on the engine of an aircraft, temperature variations range from −55 °C (in the worst case of storage before takeoff) to +200 °C (flight). Direct bonded copper (DBC) substrates are used to isolate chips (silicon dies) from their base plates. For large thermal amplitudes, the failure occurs in DBC substrates, which are copper/ceramic/copper sandwiches. The Weibull approach was used to model the brittle fracture of the ceramic layer from a natural defect. Furthermore, geometric singularities in the upper ceramic/copper interface are at the origin of cracks that grow by fatigue along the interface and finally bifurcate and break the ceramic layer. It is discussed how the framework of linear elastic fracture mechanics (LEFM) can be used to characterize the stress field around singularities and the associated risk of failure. These two criteria and the finite element method, allow analysing how a thermal loading history may modify the risk of failure of DBC substrates. It was shown, in particular, that three overcooling cycles should produce an “overload retardation effect”. Experimentally, applying three “overload cycles” (−70 °C, +180 °C), prior to thermal fatigue cycles (−30 °C, +180 °C), increased very significantly the fatigue life of DBC substrates. This result shows that the fatigue life and the reliability of power electronic devices could be optimized using a thermo-mechanical approach of the problem and suitable failure criteria.

A Thermomechanical Approach to the Formation of Dark Defects in High Power Laser Diodes

AbstractA thermomechanical model to explain the formation of dark defects in AlGaAs high power laser bars is presented. The local heating at facet defects due to nonradiative recombination and self-absorption of photons induces thermal stresses capable of producing a local plastic deformation and subsequent degradation of the device. The output power density thresholds calculated are in agreement with the data reported in the literature for these lasers.

Dynamics of double subduction: Numerical modeling

Double subduction is a geodynamic process in which two plates following each other are synchronously subducted. Double subductions are known for both modern (Izu-Bonin-Marianas and Ryukyu arcs) and ancient (West Himalaya collision zone) plate tectonics. However, our knowledge about this process is limited to conceptual schemes and some restricted analogue experiments. In order to fill this gap we performed 2D numerical experiments using a coupled petrological–thermomechanical approach based on finite differences and marker-in-cell techniques combined with thermodynamic database for the mantle. We investigated the influence of convergence rate, intermediate plate length, activation volume of the mantle dislocation creep and age of the lithosphere. Based on these experiments we conclude that: (A) Subduction rates at two zones running in parallel differ and vary in time even when the total convergence rate remains constant. Supremacy of either subduction zone depends on physical parameters such as (i) relative rates of the plates, (ii) slab ages and (iii) length of the middle plate. (B) Subduction dynamics of the double subduction system involves several processes unknown in simple subduction systems, such as (i) eduction (i.e. “un-subduction”), (ii) subduction re-initiation, (iii) subduction flip triggered by shallow slab breakoff and (iv) turn-over of detached slabs to up-side-down attitudes. (C) Simulated tomographic structures related to slab propagation account for both penetration and non-penetration of the 660 km discontinuity. Non-penetration is favored by (i) low convergence rate, (ii) faster relative movement of the overriding plate, (iii) young age of the subducting slab and (iv) up-side-down turn-over of detached slab.

A community benchmark for subduction zone modeling

We have developed a suite of benchmarks to facilitate the comparison of numerical models for the dynamics and thermal structure of subduction zones. The benchmark cases are based on a thermomechanical approach in which the slab is prescribed kinematically and the wedge flow is computed dynamically. We propose various cases to investigate the influence of boundary conditions and rheology on wedge flow and resulting thermal structure. A comparison between the codes suggest that accurate modeling of the thermal field requires a good implementation of the velocity discontinuity along the seismogenic zone and high resolution in the thermal boundary layers. A minor modification to the boundary conditions of the wedge flow is also necessary to avoid a pressure singularity that exists in analytical solutions of the cornerflow model.

Analytical modelling of electrode wear occurring during resistance spot welding

Electrode wear during resistance spot welding of galvanised steels has been modelled using an analytical thermomechanical approach. Thermal profiles in the spot weld and electrode are estimated using a one-dimensional solution. The thermal profile in the spot weld is based on a thermal balance between the material stack-up, nugget penetration and electrode geometry. Thermal profiles in the electrode are based on the results from the spot weld, as well as its relative conductivity and geometry. Results for a single weld cycle allowed prediction of a forge zone at the electrode face. Deformation of this zone under the applied stress then defined the wear and relative resultant changes in electrode geometry. Electrode life could then be predicted as a summation of these deformations from weld to weld. This was done by repeated applications of the defined equations in a spreadsheet format. Initial results were shown consistent with representative electrode life tests. The equations were then used to understand underlying physical phenomena associated with electrode wear. A discussion is also provided defining limitations to the model, and its ability to predict actual electrode life.

A thermomechanical damage approach to constitutive models for rate-independent dissipative geomaterials

This paper builds the formulations of hyperplastic damage theory for rate-independent geomaterials to describe the bulk and the likely damage behavior of granular materials. Using 2 kinematic internal variables and the conjugates, dissipative and yield function can be reasonably introduced. A systematic constitutive presentation of 32 possible ways within the thermodynamical damage framework is presented, which entirely formulates the constitutive behavior through two scalar thermodynamic potentials. Combining the four common thermodynamical energy functions, two independent kinematic internal variables and the accordingly generalized stress are introduced to describe the damage behavior and structural rearrangement of the granules for any bulk deformation. A few Legendre transformations are used to establish the links between energy functions so that the complex incremental response of geomaterials can be entirely established from these four energy functions. The constitutive relations are built with the thermodynamics laws, which account for the important structural aspects of geomaterials. Some examples are provided in the appendix to validate the applicability and implementation of the framework. This theory is based on previous work by Houlsby et al., and extends to the multi-mechanisms description. This framework paves a way in developing models for specific geomaterials with an examinable basis.

Thermal and Mechanical Couplings in Plain and Wood Fibre Reinforced Polypropylene during Tensile and Fracture Tests

The aim of this work was to show the influence of spruce fibres on polypropylene, by way of an experimental thermo-mechanical approach. These studies were performed by the simultaneous measurement of the strain field and the thermal field. A digital image correlation method was used for the strain measurements. The thermal field was obtained with the help of an infrared camera. The heat equation established in the context of classical thermodynamics of irreversible processes allowed us to evaluate the heat sources. The main difference between the plain resin and the composite material was that the heat sources dissipated by the composite were locally lower. In tensile tests the plain material allowed the creation of a neck zone with very high strain values. In fracture tests, it also generated very high strains localised at the crack tip. For the composite, the results of tensile tests showed that the presence of wood fibres led to a quasi-brittle failure of the specimen. In fracture tests, a better overstress accommodation was observed near the crack tip by distributing the strains in a wider zone.

Parametric geometry for modelling of milling operations

This paper presents a geometrical description of common end mills and of the engagement in the workpiece material for shoulder milling. The tool geometry is decomposed into elementary cutting edges in oblique cutting position and the elementary cutting forces are calculated from a thermomechanical approach and validated for a 42CrMo4 steel.

Efficient treatment of rubber friction problems in industrial applications

Friction problems involving rubber components are frequently encountered in industrial applications. Their treatment within the framework of numerical simulations by means of the Finite Element Method (FEM) is the main issue of this paper. Special emphasis is placed on the choice of a suitable material model and the formulation of a contact model specially designed for the particular characteristics of rubber friction. A coupled thermomechanical approach allows for consideration of the influence of temperature on the frictional behavior. The developed tools are implemented in the commercial FE code ABAQUS. They are validated taking the sliding motion of a rubber tread block as example. Such simulations are frequently encountered in tire design and development. The simulations are carried out with different formulations for the material and the frictional behavior. Comparison of the obtained results with experimental observations enables to judge the suitability of the applied formulations on a structural scale.

Dynamic compressive strength properties of aluminium foams. Part II—‘shock’ theory and comparison with experimental data and numerical models

One-dimensional ‘steady-shock’ models based on a rate-independent, rigid, perfectly-plastic, locking ( r- p- p- l) idealisation of the quasi-static stress–strain curves for aluminium foams are proposed for two different impact scenarios to provide a first-order understanding of the dynamic compaction process. A thermo-mechanical approach is used in the formulation of their governing equations. Predictions by the models are compared with experimental data presented in the companion paper (Part I) and with the results of finite-element simulations of two-dimensional Voronoi honeycombs. A kinematic existence condition for continuing ‘shock’ propagation in aluminium foams is established using thermodynamics arguments and its predictions compare well with the experimental data. The thermodynamics highlight the incorrect application of the global energy balance approach to describe ‘shock’ propagation in cellular solids which appears in some current literature.

A thermomechanical formulation of finite element schemes for micropolar continua

Recent studies highlighted the advantages of the thermomechanical approach for developing models of material behaviour. This approach ensures compliance with thermodynamical laws since constitutive relations are derived from a consideration of thermodynamical potentials. Interestingly, the same thermomechanical techniques can also be used to formulate the finite element models used to implement these constitutive relations. Thus the key advantage of this type of finite element formulation is that a direct link to the underlying physics of the problem is extended through to the model's implementation. Here, we show how the thermomechanical approach can be applied to finite element schemes for models based on micropolar continuum theory. Material points that make up a micropolar continuum possess rotational degrees of freedom, in addition to the conventional translational degrees of freedom. Hence, the equations governing boundary value problems for this class of materials differ from those of their classical counterparts---both from the viewpoint of the constitutive law and the governing conservation laws. We outline the development of finite element schemes for elastic and plastic micropolar materials using the thermomechanical approach. The analysis indicates that while the traditional Galerkin method admits a range of weighting functions, the second law of thermodynamics provides an additional constraint that narrows the choice of admissible functions.

Elastic/plastic models for soils and sands

Some recent advances in the constitutive modelling of soils, sands and other granular materials are reviewed. These new ideas are based on the use of the concepts of the modern theory of the thermomechanics of continua. Most existing engineering theories of soil behaviour are in the nature of “recipes”, providing rules by which yield loci, flow and hardening rules and failure lines may be constructed to provide models which predict the response and failure of granular materials in a limited set of laboratory experiments. These models rarely have any firm physical basis. The thermomechanical approach, on the other hand, enables us to construct models, which both satisfy the fundamental laws of thermodynamics and have definite physical interpretations in terms of energy storage and dissipation. Of particular importance is the distinction between the rate of plastic work and plastic dissipation, the intimate connection between dissipation and the yield loci and flow rule, and between plastic dilation and induced anisotropy. These ideas lead naturally to the concepts of critical state soil mechanics. In addition the thermomechanical approach offers the real possibility of relating the observed and simulated behaviour of granular materials on the micro- and meso-scales, to the observed behaviour at the continuum level. Some initial steps in this direction are outlined at the end of this paper.

Two-Phase Flow and the Capillarity Phenomenon in Porous Solids – A Continuum Thermomechanical Approach

Two-phase flow and capillarity phenomenon in porous solids, well known in physics and engineering, are treated from a rigorous continuum thermomechanical point of view for the first time. A ternary model, consisting of a porous solid phase, a liquid phase, and a gas phase, is investigated within the framework of thermodynamics. The main result of the evaluation of the entropy principle turns out to be that the interaction forces between the solid, gas, and liquid phases are dependent on the free Helmholtz energy functions of the corresponding phases and on the gradient of the liquid density. The classical result for the driving volume force for raising a water column in a narrow tube against the force of gravity is contained in the general investigation.

Design of stainless steel automotive exhaust manifolds

The paper deals with the design of stainless steel exhaust manifolds, focusing on the development of high temperature ferritic grades and their forming capabilities related to the new forming processes, like bending and hydroforming. In particular, it is shown along the presentation, how a niobium stabilized 14%Cr grade can be used in replacement of austenitic grades in many situations of complex shaped manifolds thanks to its combined improved formability and its high temperature resistance up to 950°C. Finally, the authors present a “virtual” thermomechanical fatigue design approach, using a dedicated post processor, which would permit to optimize the design of the fabricated exhaust manifolds, and would lower the development cost and time by limiting both the number of prototype and motor bench tests and, finally, would reduce the risk of failure.

A thermomechanical approach to the development of micropolar constitutive models of granular media

In this paper, we lay the groundwork for the development of micropolar (Cosserat) constitutive relations for granular media within the framework of the theory of thermomechanics. Expressions for the free energy and the dissipation function have been derived using a micromechanical analysis of a cluster consisting of a particle and its immediate neighbors (i.e., “the first ring”). Fluctuations in particle displacements and rotations within this mesoscale assembly as well as fluctuations in strain and curvature are represented by internal variables. Using thermomechanical techniques previously employed for classical materials, a non-local micropolar model is constructed and then subsequently applied to a granular material undergoing simple shear. The effects of the boundaries through particle rotations are discussed.

A Two-dimensional Finite Element Thermomechanical Approach to a Global Stress-Strain Analysis of Steel Continuous Casting

This paper addresses the two-dimensional finite element simulation of steel continuous casting using a global non steady-state approach. The method aims at the calculation of the thermomechanical state (temperature, deformation, stresses) of steel all along the continuous casting machine. Both plane deformation and axisymmetric versions have been developed. The first one addresses the simulation of continuous casting of slabs, taking into account the possible curvature of the machine, whereas the second one applies to cylindrical billets. The implementation of the method is validated by comparison with results from the literature. It is applied to the study of a slab continuous caster for which successive depressive and compressive stress states are revealed in the secondary cooling region.