Thermoelastic analysis of a partially insulated crack in a strip under thermal impact loading using the hyperbolic heat conduction theory

In this paper, the transient temperature and thermal stresses around a partially insulated crack in a thermoelastic strip under a temperature impact are obtained using the hyperbolic heat conduction theory. Fourier and Laplace transforms are applied and the thermal and mechanical problems are reduced to solving singular integral equations. Numerical results show that the hyperbolic heat conduction parameters, the thermal conductivity of crack faces, and the geometric size of the strip have significant influence on the dynamic temperature and stress field. The results based on hyperbolic heat conduction show much higher temperature and much more dynamic thermal stress concentrations in the very early stage of impact loading comparing to the Fourier heat conduction model. It is suggested that to design materials and structures against fracture under transient thermal loading, the hyperbolic model is more appropriate than the Fourier heat conduction model.     

Thermo-mechanical fatigue resistance characterization and materials ranking from heat-flux-controlled tests. Application to cast-irons for automotive exhaust part

In a context where the mass, the cost and the mechanical strength of materials must be jointly optimized, it is necessary to have experimental data quickly available and sufficiently robust to make efficient conception choices. For thermomechanical fatigue, standard tests usually allow comparing material for the same temperature and strain ranges although differences in thermal properties such as conductivity or thermal expansion could make significant deviations when the same thermal flux is applied particularly for structure with forced heat flux operating regimes. A new protocol is then proposed in order to compare the specific resistances of metallic materials against thermomechanical fatigue. It can easily rank materials according to their lifetime under thermomechanical loadings where strain range and temperature amplitude are determined by the heat flux applied on an industrial part. The method is based on a complete numerical analysis to determine experimental loading conditions as a temporal evolution of temperature and mechanical strain representative of thermomechanical loading observed in TMF critical areas for the part. TMF tests on hollow specimens are carried out to rank the materials: temperature and strain amplitude are different for each alloys whereas heat flux is identical. A materials ranking list based on TMF resistance is then determined according to their lifetimes under “heat-flux-controlled” tests. The method is tested for exhaust parts and demonstrates the superiority of some cast irons over others, whereas the intrinsic isotherm mechanical properties suggested an alternative classification. The obtained ranking is confirmed by experimental tests on industrial structures.     

Pressure dependence of the thermoelastic quotient for three glasses

The interrelationship between the mechanical work done on a material in the elastic range and changes in its thermodynamic properties, that is, between stress and strain, on the one hand, and temperature and entropy, on the other, is known as the Thermoelastic effect. The phenomenon is exactly adiabatic and is characterized by the thermoelastic quotient commonly referred to as thermoelastic constant. The thermoelastic effect can be used for stress analysis by monitoring the stress fluctuations by means of infrared radiometry, Also, it can be applied to study the anharmonicity in materials by measuring the temperature changes associated with adiabatic pressure changes, In this paper thermodynamic expressions are derived for the pressure derivative of the thermoelastic quotient under adiabatic as well as isothermal conditions, The derived expressions are applied to investigate the thermoelastic effect for the three glasses, namely, silica glass, soda-lime silica glass, and lead-silica glass, The isothermal pressure derivative of the thermoelastic quotient is evaluated for the three glasses. The isothermal volume derivative of the Gruneisen function is calculated.     

A new finite element for treating plane thermomechanical heterogeneous solids

This study is concerned with the development and implementation of a new finite element which is capable of treating the problem of interacting circular inhomogeneities in heterogeneous solids under mechanical and thermal loadings. The general form of the element, which is constructed from a cell containing a single circular inhomogeneity in a surrounding matrix, is derived explicitly using the complex potentials of Muskhelishvili and the Laurent series expansion method. The newly proposed eight‐noded plane element can be used to treat quite readily the two‐dimensional steady‐state heat conduction and thermoelastic problems of an elastic circular inclusion embedded in an elastic matrix with different thermomechanical properties. Moreover, the devised element may be applied to deal with arbitrarily and periodically located multiple inhomogeneities under general mechanical and thermal loading conditions using a very limited number of elements. The current element also enables the determination of the local and effective thermoelastic properties of composite materials with relative ease. Three numerical examples are given to demonstrate its versatility, accuracy and efficiency. Copyright © 1999 John Wiley & Sons. Ltd.     

Thermoelastic Phase Analysis (TPA): a new method for fatigue behaviour analysis of steels

In literature, there are already well‐established thermal methods which allow for the estimation of fatigue limit, in particular for metallic materials such as austenitic steels. These methods are based on heat source generation analysis or on surface temperature evaluation of material subjected to different types of cyclic loading. General application of methodology found limitation in those cases in which temperature changes on material related to fatigue damage were very low and, furthermore, thermal methods require high‐performance equipment and a difficult setup. This is the case, for instance, with brittle materials (such as martensitic steels), welded joints and aluminium alloys. In this work, a new thermal method named Thermoelastic Phase Analysis is used to evaluate the fatigue limit of martensitic steels. This thermal method is based on an empirical approach. The main idea is that phase of thermoelastic response of the material subjected to fatigue loading is influenced by the presence of a heat source due to dissipative phenomena related to damage. Monitoring of the phase parameter provides a more stable setup and an independent means of identifying the fatigue limit of material. The method has also proven to be potentially one order of magnitude faster than traditional thermal methods.     

Material behaviour of a dual hardening steel under thermomechanical loading

Dual hardening steels are a group of metals, which reach their material properties through a combination of strengthening via carbides and intermetallic precipitates. Because of their combination of mechanical properties, dual hardening steels are a promising alloying concept for hot‐work applications. The applied materials for hot‐work applications have to meet certain requirements, such as high hardness, high thermal strength, thermal stability, and fracture toughness. In this paper, a dual hardening steel in different heat treatment conditions was tested under out‐of‐phase thermomechanical loading conditions. All tests were done under full reverse strain control and the minimum temperature was kept constant. In the thermomechanical fatigue tests, solution annealed samples reached higher lifetimes compared with aged specimens. The hardness measurements show that the starting procedure of the thermomechanical fatigue leads to an increase of the hardness approximate to the values of the specimens with the ageing heat treatment. Cyclic softening can be observed in the test with the highest maximum temperature of 600°C. An increase of the maximum temperature also causes a decrease of the lifetime.     

Axisymmetric thermoelastic shape sensitivity analysis and its application to turbine disc design

A general method for shape design sensiti vityi analysis (SDSA) as applied to an axisymmetric thermoelasticity problem is presented using the material derivative concept and the adjoint variable method. The sensitivity of a general functional composed of thermal and mechanical quantities is considered. The method for deriving the sensitivity formula is based on standard direct thermal and elastic boundary integral equation formulation. It is then applied to obtain explicit formulas for a representative displacement and stress constraint imposed on a sector of the boundary. Results of numerical implementation are presented for weight minimization of a turbine disc under thermomechanical loading. The sensitivities of the displacement and stress constraint calculated by the formulas are compared with those by finite differences. Optimum shape obtained under the thermomechanical loading is discussed with that under the mechanical loading only, clearly showing the practical importance of the SDSA of thermoelastic systems.     

Thermomechanical behaviour of metals in cyclic loading

Temperature variation induced by repeated mechanical cyclic loading on AISI 1045 mild steel was studied.The experimental results of cyclic loading at low stress levels elucidate the coupling phenomena of thermal/mechanical behaviour which causes cooling and/or heating corresponding to the stressed state. The governing factors are thermoelastic effect and viscous dissipation. The thermoelastic effect causes the specimen temperature to go down and/or up which corresponds to the loading and/or unloading in cycling, where the viscous dissipation effect causes heat to generate inside the sample which steadily heats the specimen. As a result, a trend of increasing specimen mean temperature with periodical local fluctuation on temperature history can be observed. The heating rate, due to viscous dissipation, is increased with increasing strain rate. Cyclic loading at high stress levels results in large amounts of heat generation where thermoplasticity predominates. An abrupt temperature rise in the first few cycles, followed by a slow-down in later cycling, is to be seen. The phenomena and results were discussed. In addition, the effect of heat transfer between the specimen and its surroundings should be considered for both cases if the time is sufficiently long or the temperature gradient evolved is of significance.     

Applying infrared thermography to analyse martensitic microstructures in a Cu-Al-Be shape-memory alloy subjected to a cyclic loading

This study aims at revealing martensitic microstructures that exist in a shape-memory alloy. Infrared thermography was used for this purpose. Experiments were performed on a Cu-Al-Be single crystal which features a pseudoelastic response at ambient temperature. The specimen was first partially transformed to martensite by mechanical loading. Then a small cyclic loading was applied while the temperature evolution on the specimen surface was captured by an infrared camera. Thermal images obtained were then processed to extract two types of quantities: the maps of heat sources produced by the material and the maps of temperature oscillation amplitudes. Two thermomechanical couplings are revealed: the thermoelastic coupling and the latent heat due to the small cyclic movement of austenite-martensite interfaces, thus highlighting the martensitic microstructure distribution in the specimen.     

Experimental characterisation of a CuAg alloy for thermo‐mechanical applications. Part 1: Identifying parameters of non‐linear plasticity models

Despite the wide use of copper alloys in thermo‐mechanical applications, there is little data on their cyclic plasticity behaviour, particularly for CuAg alloys. This prevents the behaviour of the materials from being correctly described in numerical simulations for design purposes. In this work CuAg0.1 alloy used for thermo‐mechanical applications was tested by strain‐controlled cyclic loading at 3 different temperatures (room temperature, 250°C, 300°C). In each test, stress‐strain cycles were recorded until the alloy had completely stabilised. These cycles were then used to identify material parameters of non‐linear kinematic and isotropic models. The focus was on plasticity models (Armstrong‐Frederick, Chaboche, Voce) that are usually implemented in commercial finite element codes. Simulated cyclic responses with the identified material models were compared with experiments and showed a good agreement. The identified material parameters for the CuAg alloy under investigation can be used directly in finite element models for cyclic plasticity simulations, thus enabling a durability analysis of components under thermo‐mechanical loads to be performed, particularly in the field of steel‐making plants.     

Thermomechanical relaxation of residual stress in shot peened nickel base superalloy

Abstract

The thermal and thermomechanical behaviour of the relaxation of the residual stresses of a shot peened Astroloy superalloy under tensile cyclic loads has been evaluated by X-ray diffraction and investigated. The stress relaxation under purely thermal conditions (550 and 650°C) and thermomechanical conditions (pulsating tensile loading at 650°C) as afunction of the exposure time is presented. The purely thermal relaxation is interpreted by annihilation and reorganisation of the crystalline defects induced by shot peening, whereas the mechanical relaxation is linked to cyclic plasticity of materials. In consequence, the thermomechanical relaxation is essentially due to the complex mechanism of the concurrent thermal and mechanical effects. A model is used to predict the residual stresses induced by the specified shot peening conditions and their relaxation under the specified thermal/thermomechanical conditions.

MST/1963     

Thermoelastic analysis for an opening crack in an orthotropic material

The thermoelastic analysis of an opening crack embedded in an orthotropic material is made under applied uniform heat flux and mechanical loadings. To simulate the case of an opening crack filled with a medium, a thermal-medium crack model is proposed. The thermally permeable and impermeable cracks are the limiting ones of the proposed thermal-medium one. The crack-tip thermoelastic fields induced by a crack in an orthotropic material are determined in closed forms. The elastic T-stress can be also obtained explicitly. The effects of applied mechanical loadings and the thermal conductivity of crack interior on the heat flux at the crack surfaces and the mode-II stress intensity factor are investigated through numerical computations. The obtained results reveal that an increase of the thermal conductivity of crack interior decreases the mode-II stress intensity factor. And when an applied mechanical loading is increasing, the mode-II stress intensity factor is rising.     

Evaluation of damage in composites by using thermoelastic stress analysis: A promising technique to assess the stiffness degradation

The stiffness degradation represents one of the most interesting damage phenomena used for describing the fatigue behaviour of composites. A critical aspect of modelling the damage is represented by the simulation of the whole behaviour of the composite and by the assessment of the actual stiffness for the models validation. In this work, the stiffness degradation of quasi‐isotropic carbon fibre reinforced polymer (CFRP) obtained by automated fibre placement has been assessed by means of thermoelastic stress analysis. The amplitude of temperature signal at the mechanical frequency (thermoelastic signal) was considered as an indicator of material degradation and compared with the data provided by an extensometer. The correlation between thermoelastic and mechanical data allowed to build a new experimental model for evaluating and predicting material stiffness degradation by just using thermoelastic data. The proposed approach seems to be very promising for stiffness degradation assessment of real and complex mechanical components subjected to actual loading conditions.     

Response of inherently brittle materials on higher loading rates

Generally, there are components loaded in a wide spectrum of loading rates, however most of design work is based on the data obtained using quasi-statical and uniaxial loading conditions. In the case of inherently brittle materials the situation is all the more complicated because of their brittleness. Cast basalt and soda-lime glass were the main experimental materials used in this investigation as representatives of natural based and structural brittle materials. The main aim of the paper is to investigate influence of strain rate on fracture resistance and to analyze response of the microstructure to high strain rate loading including the change of mechanical properties.     

Brittle coating studies on fibrous composites

A brittle coating stress analysis technique applicable to orthotropic materials has been developed. The technique has been applied to a unidirectional glass fibre reinforced epoxy. Its behaviour has been studied under uniaxial and biaxial stress fields using cantilever beam specimens and circular disc specimens under diametral compression. Fibre orientation in the specimens has been varied. In each case it has been observed that the cracks represent the direction of principal strains in the specimen material and not the direction of principal stresses. Application of brittle coating techniques has been suggested to establish the direction and magnitude of principal stresses and strains at every point in a problem with unknown stresses and strains.     

Thermal effect of plastic dissipation at the crack tip on the stress intensity factor under cyclic loading

Plastic dissipation at the crack tip under cyclic loading is responsible for the creation of an heterogeneous temperature field around the crack tip. A thermomechanical model is proposed in this paper for the theoretical problem of an infinite plate with a semi-infinite through crack under mode I cyclic loading both in plane stress or in plane strain condition. It is assumed that the heat source is located in the reverse cyclic plastic zone. The proposed analytical solution of the thermo-mechanical problem shows that the crack tip is under compression due to thermal stresses coming from the heterogeneous stress field around the crack tip. The effect of this stress field on the stress intensity factor (its maximum and its range) is calculated analytically for the infinite plate and by finite element analysis. The heat flux within the reverse cyclic plastic zone is the key parameter to quantify the effect of dissipation at the crack tip on the stress intensity factor.     

Tensile strength of the brittle materials, probabilistic or deterministic approach?

For various loading rates we estimated the activated defect localization in Modified Brazilian Disk type glass specimens in comparison with standard spherical glass specimens. Specimen geometry can considerably affect the mechanical response of material, especially brittle ones, which are very sensitive to the distribution of defects. High and low loading rates of Modified Brazilian Disk lead glass specimens have been investigated using universal Instron test machine and compressive Hopkinson pressure bars. The experimental results obtained have been compared using the Weibull distribution for scatter strength variation. Stress distribution in the above specimens was calculated using the finite element method, which provided detailed analysis of the macromechanical brittle fracture mechanism. In static tests of spherical glass specimens, we observed generation of contact stresses, which result in activation of defects in the working parts of specimens, whereas no activated defects were observed in Modified Brazilian Disk specimens neither under static, nor under dynamic loading conditions. For specimens of various geometries and type of load application it is recommended to apply probabilistic approaches, e.g., the Weibull approach, insofar as contact stresses in brittle materials induce activation of defects, location of which depends on the specimen geometry and loading type. __________ Translated from Problemy Prochnosti, No. 1, pp. 100–115, January–February, 2006.     

脆性材料在双向应力下的断裂和失效研究

采用热力学方法对脆性薄片试样成功地进行了双向和单向平面拉伸试验,通过观察和记录试片中心的直通裂纹的扩展和断裂过程,测试出玻璃和陶瓷薄片的断裂韧性在双向和单向拉伸载荷时的差别．结果表明双向拉伸使裂纹阻力增强,平行于裂纹的应力对裂纹扩展有影响．该研究表明,对线弹性材料在双向载荷作用下,传统的应力强度因子准则不适用．裂纹张开的应变依赖性被证实在双向应力的断裂评价中．     

A reliability analysis method in thermomechanical fatigue design

The design of structures against thermomechanical fatigue (TMF) is a relatively new concern and research has generally concentrated on deterministic methods to ensure the resistance of structures undergoing thermal–mechanical loadings. Many studies have thus been conducted to better represent the nonlinear behaviour of materials or to develop thermomechanical fatigue criteria. However, fatigue is a phenomenon which is random in nature: manufacturing processes, geometric tolerances and usage conditions can affect the lifetime of a structure. Typically, the use of a car by a customer is unique (type of roads, weather conditions, drivers behaviour, etc.) and thus thermomechanical loads for instance on a cylinder head become probabilistic. Similarly, the intrinsic strength of a structure is variable (casting and machining process, specific microstructures, etc.). It is therefore necessary to be able to guarantee the TMF resistance of a particular structure itself undergoing a particular load, whatever the structure is. The work presented here consists of the development of a complete protocol analysis of the risk of failure of a structure subjected to thermomechanical fatigue when either exact loading conditions or strength for a given structure are uncertain. The proposed method relies on the stress–strength interference analysis and also on numerical techniques based on finite element calculation and engine load analysis which enable us to compute a local damage from a global loading. The method is successfully applied to a cylinder head.