Modeling of residual stresses variation with thermal cycling in thermal barrier coatings

Thermal barrier coatings (TBCs) are commonly used as protective coatings for engine metal components to improve performance. Many investigations have shown that residual stresses in TBCs applications play an important role, but the residual stresses are mainly obtained by simulation method. As we know, there are a few analytical solutions of residual stress in TBCs system. In this paper, a new two-dimensional analytical solution has been obtained under the condition of non-linear coupled effects of temperature gradient, thermal fatigue, deposited residual stress, thermally grown oxide (TGO) thickening, elasto-plasticity deformation and creep deformation of TBC. Moreover, the influences of bending moment and curvature on stress variation in TBCs are considered during thermal cycling. The calculated results are in agreement with the prior experimental results.     

Residual/thermal stresses in FGM and laminated thermal barrier coatings

The plane strain elasticity problem for a functionally gradient material (FGM) and a multi-layered homogeneous coating bonded to a metal substrate due to a uniform temperature change is considered. The substrate is assumed to be a nickel-based alloy-Rene-41. The FGM coating is a particulate composite of Rene-41 and zirconia with volume fractions continuously varying through the thickness. The multi-layered coating consists of one, two or four homogeneous layers with stepwise changing volume fractions. With a possible failure mechanism of surface cracking or edge debonding in mind, the relevant stresses on the surface of the coating and along the interfaces are evaluated. For the piecewise homogeneous coating the power of singularity and the corresponding stress intensity factors at the points of intersection of the interfaces and the free ends are calculated. It is shown that by using the FGM coating the stress singularities are eliminated and the stress distribution is smoothed considerably. Sample results for the displacements and for the contour plots of an effective stress governing the yield behavior of the material are given and the asymptotic behavior of the stress state around the singular point is examined.     

Statistical analysis of microhardness variations in thermal spray coatings

A thermal barrier coating system consisting of a NiCoCrAlY bond coat and cerium-stabilized zirconia ceramic coating was sprayed on to a metallic substrate. Ageing at 400 and 800°C for 100, 500, and 1000 h was performed. Microhardness measurements of as-sprayed and heat-treated samples were used to evaluate microstructural variations throughout the thermally sprayed coating after different ageing conditions. Forty readings were taken at both the bond coat and ceramic coating positions within the thermal barrier coating (TBC) system and adjusted by subtracting the two largest and two smallest readings. Both data sets were statistically analysed to assess whether they belonged to Weibull or Gaussian (or normal) distributions. This study has established that the homogeneity of coatings, at least as measured by a microhardness test, varies during service and, thus, may influence the lifetime.Nomenclature Confidence limit - Mean value - Standard deviation - ² Variance - Weibull modulus obtained from any method - Characteristic value obtained from any method - CV Coefficient of variation - f(x) Probability density function - F(x) Cumulative density function - i ith order in ascending data set - L Log-likelihood function - m Weibull modulus - n Total number of data points - x Microhardness data - x _i Microhardness data which is ith order in ascending data set - x ₀ Characteristic value which gives 63.2% cumulative density     

Influences on development of thermal and residual stresses in quenched steel cylinders of different dimensions

Abstract

In the numerical treatment of thermal and transformation stresses produced during quenching, and of the resulting residual stresses, calculations carried out using computer programs are for economic reasons restricted to simple geometries such as infinite plates or cylinders. Difficulties arise when results so obtained are applied to real components. The effects of geometric discontinuities, for example near the top and bottom of a cylinder, need further systematic investigation. In this paper, stress distributions in steel cylinders of different diameters, quenched with and without transformation effects from different temperatures, are calculated using a finite–element program; the differences revealed in the local stress states are discussed. Results of special calculations making use of different boundary conditions are introduced, allowing the important mechanical and thermal factors that influence the final residual–stress states to be assessed. These results allow the validity of assumptions necessary in the analytical computations to be estimated realistically.

MST/1     

Effects of grinding process on residual stresses in nanostructured ceramic coatings

This paper investigates the depth profiles of residual stresses using the sin² method combined with grazing incident X-ray diffraction (GIXD) technique. It specifically focuses on the effects of grinding process on the residual stresses in the thermally sprayed nanostructured WC/12Co and Al₂O₃/13TiO₂ (n-WC/12Co and n-Al₂O₃/13TiO₂) coatings on low carbon steel substrates. The influence of grinding parameters, such as depth of cut (DOC), table feedrate, abrasive grit size and wheel bond type, on residual stresses is studied. The conditions and limitations of X-ray diffractometry for residual stress measurements are discussed. Discussed also is the difference between the average and actual depth profiles of residual stresses. The paper introduces a method for retrieving the actual depth profiles from the measured average depth profiles. Finally, the influence of peak broadening of grain size, anisotropy from different diffraction planes and surface finish of the samples on the measurement results is explored.     

Aspects of residual thermal stresses in continuous-fibre-reinforced ceramic matrix composites

An analytical model is presented that predicts the thermal stresses which arise from mismatch in coefficients of thermal expansion between a fibre and the surrounding matrix in a continuous fibre composite. The model consists of two coaxial isotropic cylinders. Stress transfer between the fibre and the matrix near an unstressed free surface has been modelled by means of a shear-lag analysis. Away from the free surface the theoretical approach satisfies exactly the conditions for equilibrium and continuity of stress at the fibre-matrix interface. Application of the model to a composite consisting of a glass-ceramic calcium alumino-silicate (CAS) matrix containing unidirectional Nicalon fibres points to a strong dependence of stress on fibre volume fraction. Surface effects are significant for depths of the order of one fibre diameter. Near-surface shear stresses resulting from cooling from the stress-free temperature are sufficiently high to suggest that a portion of fibre close to the surface is debonded at room temperature. Experimental results acquired with a scanning electron microscope (SEM) equipped with a heating stage are consistent with this prediction. Consequently, the model has been modified in a simple way to incorporate frictional slip at the interface, according to the Coulomb friction law. Although detailed measurements are limited by the resolution of the technique, experimental evidence suggests that the transfer length is within an order of magnitude of the model prediction.     

The treatment of thermal and residual stresses in fracture assessments

The behaviour of a crack under combined mechanical and thermal/residual loads is described in terms of a reference stress or equivalent mechanical loading. The reference stress can be readily established from a knowledge of the stress intensity factor for the thermal/residual load, the magnitude of the mechanical load, and the material stress-strain curve. The result enables the J-integral to be evaluated and is also used to define a procedure for the inclusion of thermal/residual stresses in the CEGB defect assessment method (R6). In particular, a detailed procedure is given for treating thermal/residual stresses in recent revisions of R6 which cater for structures made of materials which strongly work-harden.     

Non-destructive identification of residual stresses in steel under thermal loadings

We discuss computational aspects of the inverse and ill-posed problem of identifying residual stresses in steel structures under thermal loading. This corresponds to an inverse source problem in linear thermo-elasticity. The studies aim in investigating whether thermal loadings for the excitation of structures are sufficient in order to detect reliably inherent residual stresses. These stresses may result from the construction process or later thermal or mechanical treatment of the structure-like welding. By answering the raised question positively, our method provides an important basis for successful thermal straightenings. The quality of the solution of the inverse problem depends on a series of parameters, like material parameters, noise in the measurements, and the experimental setup. We numerically study the effects of these parameters and quantify the uncertainties in the results of the inverse problems by means of Sobol indices.     

Microstructural influence on erosion behaviour of thermal spray coatings

The influence of structure on erosion performance of thermally sprayed Cr₃C₂–NiCr coatings under industrial turbine conditions has been investigated. Thermal spraying of these materials results in substantial variation in composition and microstructure due to exposure of the coating powders to the high temperature accelerating gas.Coatings were characterised using Back Scatter Electron imaging in conjunction with X-ray diffraction which showed carbide dissolution into the matrix of varying extent depending on deposition technique. Heat treatment at 900 °C caused carbide precipitation and matrix refinement. Erosion testing of as-sprayed and heat treated coatings was conducted at ambient and elevated temperature. Single impacts were characterised using Scanning Electron Microscopy in order to determine the erosion mechanism.At ambient temperature the single impacts caused a brittle response with both carbide grains and matrix being cleaved by the erodent particle. Brittle cracks surrounded each impact and intersected with splat boundaries leading to a significant contribution to erosion rate from splat structure. Following heat treatment the erosion response of the coatings was more ductile with mounds of plastically deformed material surrounding each impact, this significantly reduced erosion rate.     

Formation of residual stresses in coatings during high-energy treatment: A survey

The appearance of residual stresses in metals is one of the effects accompanying the action of high-energy treatment. Under both electrospark and laser treatments, temperature is a prevailing factor affecting the formation of residual stresses. High rates of heating and cooling of a metal in the melting zone result in the appearance of thermal stresses determined by the difference between the coefficients of thermal expansion of the metal. A combined electrospark and laser treatment creates a stressed state in the surface layer with better characteristics than each treatment does separately. The value, sign, and distribution of the residual stresses substantially influence the service properties of machine parts. Frantsevich Institute of Problems of Materials Science, Ukrainian Academy of Sciences, Kiev. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 35, No. 6, pp. 72–78, November–December, 1999.     

Application of reaction synthesis principles to thermal spray coatings

Reaction synthesis principles have been extended to plasma spraying to obtain coatings consisting of mixed oxide phases and iron aluminides. Elemental powders of iron and aluminium were fed through a d.c. plasma torch to deposit intermetallic coatings on carbon steel substrates. Carbon steel substrates were also pre-heated with a plasma flame to create an iron oxide surface on the substrate such that an exothermic thermite reaction takes place when molten splats of aluminium impinge the pre-heated substrate at sub- or supersonic velocities. A thermite reaction between iron oxide and aluminium allowed the formation of alumina, FeAl2O4, iron, and iron aluminide phases. The presence of FeAl2O4 and Al2O3 increased the surface hardnesses of the coating, and the hardnesses of the coatings are significantly higher than the hardnesses of steel substrate, and aluminium particles. X-ray analysis of the coatings, microstructural observations, and microhardness measurements suggest that plasma spraying conditions can be tailored to obtain coatings with high hardness values with in situ synthesized reinforcements (spinel and alumina) or iron aluminide phases. Aluminium-rich phases were observed in the as-deposited coatings when a mixture of aluminium and iron or aluminium and nickel were fed through the plasma gun in ratios equivalent to Fe3Al, FeAl, Ni3Al, and NiAl. In some cases, annealing allowed the formation of iron-rich or nickel-rich aluminide phases. High solidification rates of molten splats allowed very limited diffusional reactions between the splats of aluminium and iron, or aluminium and nickel because the available diffusional time for exothermic interfacial reactions is limited to a fraction of a second at best. Oxidation of part of the aluminium led to the formation of alumina in the as-deposited coatings, and therefore, a vacuum plasma spraying technique is desirable to obtain intermetallic phases. The results suggest that reactive spraying will allow deposition of coatings by utilizing the heats of reaction between the constituents, and reactive spraying will broaden the engineering applications of reaction synthesis techniques.     

Matrix solidification and the resulting residual thermal stresses in composites

The disparate thermal expansion properties of the fibres and matrices in high-performance composites lead to an inevitable build up of residual thermal stresses during fabrication. We first discuss the thermal expansion behaviour of thermoplastic and thermoset polymers that may be used as high-performance composite matrices. The three classes of polymers considered are epoxies, amorphous thermoplastics, and semicrystalline thermoplastics. The relevant thermal expansion data for prediction of the magnitude of the residual stresses in composites is the zero (atmospheric)-pressure thermal expansion data; these data are plotted for a range of thermoplastics and a typical epoxy. Using the technique of photoelasticity, we have measured the magnitude of the residual stresses in unidirectional graphite composites with an amorphous thermoplastic matrix (polysulfone) and with an epoxy matrix (BP907). The temperature dependence of the residual stress build up and the resulting magnitude of the residual stresses correlate well with the thermal and physical properties of the matrix resin.