Calculation Of Residual Stresses Research Articles

Microstructure and elastic properties of atomic layer deposited TiO 2 anatase thin films

Amorphous TiO 2 thin films were deposited by means of atomic layer deposition on Kapton substrates and then crystallized ex situ by annealing at 300 °C to obtain the anatase phase. The morphology, structure and microstructure of films treated for 12, 24, 72 and 90 h were investigated. The local Ti coordination changes were studied by X-ray near-edge structure (XANES). On the basis of X-ray diffraction residual stress calculations, the elastic anisotropy of the films is experimentally determined for the first time ( A comp ∗ = 0.07 , A shear ∗ = 0.03 ). The film macro-strains increased with the time of treatment, while the micro-strains decreased. This effect may be correlated with the incipient anatase-to-rutile transformation as suggested by the changes observed in the XANES pattern of the film treated for 90 h. However, the contribution of the substrate cannot be excluded.

An Image-Based Microscale Simulation of Thermal Residual Stresses in DSE Oxide Ceramic Composite

An image-based microscale analysis was conducted by using finite element method (FEM) to simulate the thermal residual stresses in directionally solidified eutectic (DSE) oxide ceramic composites from the thermal expansion and elastic properties and the microstructure features of the constituent phases. This microscale analysis allows a real simulation of morphologies of constituent phases such as size, array and shape. Meanwhile, this model can be applied not only for the calculation of thermal residual stresses, but also for the calculation of mechanical properties. In this work, simulations focus on the distribution of thermal residual stresses in the directionally solidified eutectic (DSE) Al2O3/ Y3Al5O12 (YAG) ceramic composite. A good agreement between simulated and measured thermal residual stresses was observed.

Theoretical Calculation and Numerical Analysis of Residual Stress in Laser Peen Forming of Metal Plate

Laser peen forming is an emerging novel process of metal plate bending, which uses laser-induced shock wave pressure to generate an unbalanced residual stress field in the target, the moment of the residual stress causes metal plate to develop plastic bending deformation. The mechanism of laser shock induced residual stress was introduced firstly, then the deforming process of metal plate induced by residual stresses was discussed and the depth of the residual compressive stress was proposed. Effects of processing parameters on the residual stress distribution and plate bending deformation were numerical analyzed. The results indicated that the bending deformation of sheet was relative to laser peening numbers, peening coverage and thickness of plate, the magnitude and distribution of residual stresses could be precisely controlled by adjusting laser processing parameters.

Residual stress evaluation at the micrometer scale: Analysis of thin coatings by FIB milling and digital image correlation

In this report, an optimised method for residual stress determination at the microscopic scale is presented. The newly proposed approach involves incremental Focused Ion Beam (FIB) milling of annular trenches at material surface, combined with high resolution SEM imaging of a previously deposited marker pattern. Digital image correlation (DIC) analysis of the relative displacements between markers with respect to the undisturbed state provides a measure of strain relief. Results of finite element modeling show that the proposed configuration gives complete strain relief when the annular trench depth becomes comparable with the diameter of the remaining stub, thus allowing analytical calculation of the average residual stress from measured strain components. Basing on results of modeling, the experimental methodology has been developed and optimised for residual stress analysis in thin coatings. In order to cover a wide range of material properties and residual stress states, two different materials have been selected: TiN CAE-PVD coating (hard and stiff, with compressive residual stress) on WC–Co substrate, and also an Au MS-PVD coating (soft and compliant, with tensile residual stress). The procedure for the optimization of FIB milling parameters is reported. Results are validated by comparison with residual stress evaluation by X-ray diffraction and curvature measurement on the two different specifically selected PVD coatings.

Superficial quenching of mechanical pieces and calculation of residual stresses: modeling and simulation

Hardening of steel after induction surface heating is studied. Amodel of the process of hardening of a cylinder is created and subjected to numerical simulation in order to determine the stresses formed in the part. Two principal methods for describing the variation of the stress state during the treatment are developed. Residual stresses are analyzed in both models and compared with the results of an x-ray study. The correlation between the measured data and the numerical results is discussed.

Internal Residual Stress Measurements in a Bioactive Glass–Ceramic Using Vickers Indentation

The residual stress distribution that arises in the glass matrix during cooling of a partially crystallized 17.2Na2O–32.1CaO–48.1SiO2–2.5P2O5 (mol%) bioactive glass–ceramic was measured using the Vickers indentation method proposed by Zeng and Rowcliffe (ZR). The magnitude of the determined residual stress at the crystal/glass boundary was 1/4–1/3 of the values measured using X‐ray diffraction (within the crystals) and calculated using Selsing's model. A correction for the crack geometry factor, assuming a semi‐elliptical shape, is proposed and then good agreement between experimental and theoretical values is found. Thus, if the actual crack geometry is taken into account, the indentation technique of ZR can be successfully used. In addition, a numerical model for the calculation of residual stresses that takes into account the hemispherical shape of the crystalline precipitates at a free surface was developed. The result is that near the sample surface, the radial component of the residual stress is increased by 70% in comparison with the residual stress calculated by Selsing's model.

Failure Mechanisms of PVD Films on Organic Coatings

Physical vapour deposited (PVD) films have many benefits as coatings on metals but provide little corrosion resistance or surface levelling of the underlying substrate. This research investigates the use of epoxy undercoats for PVD films as a means of overcoming these deficiencies. Experimental trials showed that sputtered titanium films and the epoxy undercoats both cracked severely as a result of the PVD process. A quantitative model has been developed for the calculation of residual stress in a three-layer film-epoxy-substrate system. The model and experimental trials showed that cracking originated from thermal stresses developed in the titanium-epoxy-aluminium system as a result of PVD. Instability and cracking initiated where pores intersected the film-coating interface. Increasing the baking temperature to 210oC raised the tensile strength of the epoxy sufficiently to avoid instability due to residual stress and produce crack-free PVD titanium films.

Birefringence simulations for annealed ingots of the -and - growth calcium fluoride single crystals with consideration of creep deformation

We developed an analysis system for simulating birefringence of an annealed ingot of CaF2 single crystal caused by the residual stress after annealing process. The analysis system comprises the heat conduction analysis that provides the temperature distribution during the ingot annealing, the stress analysis to calculate the residual stress after ingot annealing, and the birefringence analysis of an annealed ingot induced by the residual stress. The finite element method was applied to the heat conduction analysis and the stress analysis. In these analyses, the temperature dependence of material properties and the crystal anisotropy were taken into account. In the residual stress calculation, we considered the time-dependent nonlinear deformation behavior of a material called creep. In the birefringence analysis, the distributions of optical path difference were calculated by using average stress method with consideration of the crystal anisotropy. We can perform the birefringence analysis of an ingot of CaF2 single crystal with any growth direction, using this analysis system, and we performed the analyses of the crystals with the <001> and <111> growth directions. From these analyses, we obtained reasonable results of optical path difference in comparison with the experimental results.

Calculation and experimental determinations of the residual stress distribution in alumina/Ni/alumina and alumina/Ni/nickel alloy systems

Residual stress problems encountered in joining ceramics–ceramics or ceramics–metals systems for high-temperature applications >1000 °C have been studied. A solid-state bonding technique under hot-pressing via metallic foils sheet of Ni was used for joining alumina–alumina and alumina–nickel alloy (HAYNES® 214™). The residual stresses expected in the specimen were predicted by finite-element method (FEM) calculations using an elastic–plastic-creep model (EPC). Stress distributions in the specimen were characterized experimentally using X-ray diffraction (XRD) and Vickers Indentation Fracture (VIF) techniques. The tensile and shear stress profiles have been determined along selected lines perpendicular to the bonding interface. The results of the FEM calculation of residual stresses have been compared experimentally with the results of classical XRD and indentation methods. It was found that the tensile stress concentration showed higher values at the edge of the boundary. The residual stresses caused by the thermal expansion mismatch between alumina (Al2O3) and Ni-based super-alloy (HAYNES® 214™) severely deteriorated the joints compared to Al2O3–Al2O3 joint with the same solid-state bonding parameters. The correlations between the FEM calculations and experimental results obtained by XRD and VIF method were discussed.

Computational Study on the Fatigue Behavior of Welded Structures

The major objective of this study is to develop a computational fatigue test method for welded structures. The damage mechanics approach is used to derive explicit expressions for fatigue life estimation within the framework of continuum mechanics. Microdamage model is applied to calculate the quasi-brittle material damage prior to the crack initiation. Based on the two-scale model, that is, micro versus meso (macro) scale linkage scheme is implemented in conjunction with finite element method to describe the crack initiation or propagation. For the material damage model used at microscale, a finite element code is developed. Lemaitre’s unified damage model and constitutive equation were chosen so as to ensure the efficiency for developing finite element algorithm. Identification method for material parameters required to constitutive equation is proposed using inversion of Ramberg-Osgood type constitutive model. In order to consider weld-induced residual stresses, the Ueda’s inherent strain scheme is incorporated into the calculation of residual stresses. Computational procedure based on two-scale model with the use of commercial finite element code is successfully constructed. The numerical results obtained by proposed method are compared with experimental results for validation.

Texture and Strain Experiments at OPAL

In response to the development of new materials and the application of materials and components in new technologies the direct measurement, calculation and evaluation of textures and residual stresses has gained worldwide significance in recent years. Non-destructive analysis for phase specific residual stresses and textures is only possible by means of diffraction methods. The determination of global texture and the local variation of texture for example by inhomogeneous deformation are very important due to the coherence between the texture and the physical and mechanical properties of materials.

Calculation and Experimental Verification of Residual Stresses in Riveted Joints Used in an Airframe

This paper presents diffraction measurements of residual stresses around the rivet, formed during the riveting process. The measurements were made with the XSTRESS-3000 diffractometer, manufactured by Stresstech Oy. The measurements were carried out on specimens made of bare sheet 2024-T3 alloy, (standard AMS-QQ-250 / 4). The measurement results were compared with the FEM simulation results.

Assessment of residual thermal stresses in polycrystalline aggregates of carbide grains of WC-Co hard alloy

An algorithm of the calculation of residual thermal stresses in WC polycrystalline aggregates of WC-Co hard alloy has been considered. The equations of thermoelasticity have been used as the basis for the algorithm. Stresses, in a polycrystal are generated due to anisotropy of the thermal expansion of single-crystalline grains and misorientation of crystallographic axes of neighboring grains as well as stresses that are transmitted to the aggregate from the surrounding hard alloy, have been calculated. The results obtained are comparable to the experimental data.

Determination of global and local residual stresses in SOFC by X-ray diffraction

Solid Oxide Fuel Cell (SOFC) is a high-performance electrochemical device for energy conversion. A single cell is composed of five layers made of different ceramic materials: anode support, anode functional layer, electrolyte, cathode functional layer and cathode. The mechanical integrity of the cell is a major issue during its lifetime, especially for the electrolyte layer. Damage of the cells is mainly due to the high operating temperature, the “redox” behaviour of the anode and the brittleness of the involved materials. Since residual stresses are known to play a significant role in the damage evolution, it is important to determine them. For this purpose, residual stresses in an anode-supported planar SOFC were measured by X-ray diffraction. Firstly, macroscopic stresses in each phase of each layer were studied using the sin 2 ψ method on a laboratory X-ray goniometer at room temperature. This technique enables the calculation of residual stress of the material from the measurement of the crystal lattice deformation. The electrolyte has been found under bi-axial compressive stress of −920 MPa. Secondly, X-ray measurements controlling depth penetration were made in the electrolyte using grazing incidence method. The results show that the stress is not homogenous in the layer. The first five micrometers of the electrolyte have been found less constrained (−750 MPa) than the complete layer, suggesting a gradient of deformation in the electrolyte from the interface with the Anode Functional Layer to the free surface. Finally, local stress measurements were made on the electrolyte layer by X-ray synchrotron radiation that allows high accuracy measurement on the (sub-) micrometer scale. Polychromatic and monochromatic beams are used to determine the complete strain tensor from grain to grain in the electrolyte. First results confirm the macroscopic stress trend of the electrolyte. These X-ray techniques at different scales will contribute to a better understanding of the residual stress in the electrolyte layer and thus to the involved damage mechanisms.

Raising of a heavy semi-circular vault on a rigid centering

The modelling of a process of a semi-circular vault raising on a rigid cylindrical centering is conducted. Within the bounds of accreted solids mechanics the evolution of the vault stress-strain state under gravity action during the raising and after its completion is investigated. The vault material is described with defining relationships for elastic or aging viscoelastic materials. The formulation of the non-classical quasi-static initial-boundary accretion problem is given. Its analytical solution in series and quadratures is built. An effective method of calculation of residual stresses in the finished vault after supporting centering removing is offered.

Prediction of the Residual Stress in Grind-Hardening with Thermal-Mechanical-Phase Transformation Stress Coupled Analysis

Grind-hardening is a type of composite technology, which utilizes the dissipated heat in the grinding zone for hardening of the workpiece surface layer. The temperature of the workpiece surface, when heated by the grinding, is higher than the austenitizing temperature for short time, then it is lowered by quick cooling causing martensitic transformation to happen in the surface layer of the workpiece. The residual stress is formed by the thermal stress, phase transformation stress and mechanical stress in the grind-hardening layer. In this paper, the forming mechanism of the residual stress in grind-hardening technology is analyzed in theory; the residual stress field in the surface layer is calculated by the finite element, according to changes in the specific volume of the microstructure, the temperature field and the temperature history of the surface layer at different depths. The temperature field is achieved by computer simulation technology. The result of residual stress calculations indicates that the change tendency of the grind-hardening residual stress in the finite element analysis is consistent with the experiments.

Early-age acoustic emission measurements in hydrating cement paste: Evidence for cavitation during solidification due to self-desiccation

In this study, the acoustic emission activity of cement pastes was investigated during the first day of hydration. Deaired, fresh cement pastes were cast in sealed sample holders designed to minimize friction and restraint. The majority of acoustic emission events occurred in lower water to cement ratio pastes, while cement pastes with higher water to cement ratios showed significantly less acoustic activity. These acoustic events occurred around the time of setting. A layer of water on the surface of the cement pastes substantially reduced acoustic emission activity at the time of setting. According to these experimental results, the acoustic emission measured around setting time was attributed to cavitation events occurring in the pores of the cement paste due to self-desiccation. This paper shows how acoustic emission might be used to indicate the time when the fluid–solid transition occurs in a cement paste, often referred to as time-zero. Knowledge of time-zero is fundamental for determining when mechanical properties develop and in calculations of residual stresses.

Joining of ZrB2‐Based Ultra‐High‐Temperature Ceramic Composites to Cu–Clad–Molybdenum for Advanced Aerospace Applications

Three hot‐pressed ZrB2‐based ultra‐high‐temperature ceramic composites (UHTCC), ZrB2–SiCp(ZS), ZrB2–SiCp–C (ZSC), and ZrB2–SCS9A (SiC fiber)–SiCp(ZSS), were joined to Cu–clad–Mo using AgCuTi brazes (TL∼1073–1173K) and Pd‐base brazes (TL∼1493–1513K). More extensive chemical interactions occurred in Pd‐base joints than in AgCuTi‐base joints. The Pd‐braze region displayed higher hardness in joints made using ZS than ZSS and ZSC. Residual stress calculations point toward negative strain energy up to ∼23% clad layer thickness because αCu–clad–Mo&lt;αZS(α=coefficients of thermal expansion). Above this thickness, αCu–clad–Mo&gt;αZS, strain energy is positive, and it increases with increasing thickness. Projected reductions in the thermal resistance highlight the benefits of joining the UHTCC to Cu–clad–Mo.

The NeT bead-on-plate benchmark for weld residual stress simulation

Fracture mechanics based structural integrity assessments of pressure vessels and piping are widely used to support the economic and safe management of operating engineering plant. Assessments of defects at weldments can be highly sensitive to the through-thickness distribution of residual stress assumed in the fracture calculations. Increasingly, finite element modelling approaches are applied to predict residual stress in engineering structures arising from the welding process. However, such methods are complex and require analysts to make many assumptions and approximations. Guidelines covering the calculation of residual stresses in weldments are being prepared for inclusion in the R6 defect assessment procedure and will be accompanied by a series of validation benchmarks. The benchmarks will allow analysts to evaluate and improve the accuracy of weld modelling approaches and assess their suitability for use in fracture assessments. The first part of this paper presents an austenitic stainless steel bead-on-plate weldment validation benchmark based on the extensive round robin measurements performed by members of the European NeT project. The benchmark defines thermal and residual stress performance targets against which a weld simulation approach can be evaluated. Guidance is also provided on how to validate predicted residual stress profiles for use in a high integrity fracture assessment. The second part of this paper provides a commentary on how the weld simulation accuracy and performance targets have been established.

Measurement and calculation of thermal residual stress in fiber reinforced ceramic matrix composites

In this study, thermal residual stresses in two SiC-ceramic matrix composites reinforced with carbon fiber (C/SiC) and silicon carbide fiber (SiC/SiC) were completely investigated. Thermal residual stress in the C/SiC was quantified by three different methods of experimental measurement, analytical calculation, and theoretical prediction, and then compared with that in the SiC/SiC. Good agreement between these methods was observed and their applicability to the present composite systems was validated. Relationships between the thermal residual stress state and macroscopic mechanical properties of the composites (e.g., the first matrix cracking stress) are discussed.