Effect of quartz particle size on the mechanical behaviour of porcelain tile subjected to different cooling rates

Porcelain tile is a high-performance ceramic tile, in which quartz is a major compositional component. After the firing cycle, macroscopic residual stresses develop in the product as a result of rapid cooling. Further, during cooling, the presence of quartz particles also increases natural flaw size. Both phenomena significantly affect the product's mechanical behaviour. This study examines the effect of quartz particle size on the mechanical behaviour of porcelain tile subjected to two very different cooling rates: a rapid or a slow cooling rate. A series of porcelain tile compositions were designed for this purpose, in which quartz particle size was varied. The mechanical behaviour of the sintered pieces was evaluated on the basis of linear elastic fracture mechanics. It was verified that, in the slowly cooled material, the modulus of elasticity and fracture energy increased, and natural flaw size decreased as quartz particle size decreased. However, fracture energy also diminished in pieces that contained excessively small particles, with an advanced state of dissolution. For the rapidly cooled material, though the larger sized quartz particles debonded at higher temperatures owing to thermal stress, their presence, even in small quantities, contributed to natural flaw growth. The lower fracture energy associated with this last type of piece also favours this phenomenon.     

Delayed curvature and residual stresses in porcelain tiles

Most industrial porcelain tiles suffer changes in their curvature after firing: such process is known as delayed curvature. One of the hypotheses used to explain this phenomenon is based on the relaxation of residual stresses by creep. In this study two types of industrial glazed porcelain tiles have been studied. One of them displayed delayed curvature after firing, whereas the other one presented a stable curvature. The main objective was to determine if the delayed curvatures were caused by the residual stresses generated during rapid industrial cooling. Both types of existing residual stresses (thermal stresses, caused by thermal gradients inside the tile during cooling, and body–glaze fit stresses, due to the thermal expansion mismatch between body and glaze) were measured, as well as related samples properties (elastic modulus, creep behaviour, thermal expansion). The results demonstrated that the residual stresses are not the main cause of the delayed curvature phenomenon.     

Process-induced residual stresses in compression molded UHMWPE

Non-isothermal cooling during processing causes the development of residual stresses, which are analyzed for compression molded UHMWPE, and affects the dimensional stability. The development of thermal residual stresses was predicted using an incremental stress analysis that included temperature-dependent material properties. Strain gauges were used to measure the residual stresses as layers were removed from a molded disk using a Process Simulated Laminate (PSL) approach. The PSL technique has not previously been applied to a compression molded neat polymer. For initial surface cooling rates of ～ 11°C/min, the model predicted a compressive stress at the bottom surface of 14 MPa and a tensile stress near the center of 2.5 MPa and matched the experimental distribution well. Because the compressive residual stress was 70% of the yield strength (～20 MPa), a lower cooling rate was also tested (2.6°C/min). The maximum tensile and compressive stresses for this cooling rate were, 0.91 MPa and 2.5 MPa, respectively. The model demonstrated its use for predicting thermal residual stresses in compression molded parts, instead of trial-and-error experimentation. UHMWPE is shown to develop residual stresses continually from ～ 120°C to 23°C.     

Residual Stress Analysis of Commercial Float Glass Using Digital Photoelasticity

Residual stresses are generated in float glass at the time of manufacturing due to thermal gradients created during the cooling process. The quantification of these residual stresses is important in glass industries as they affect their cutting quality. Photoelasticity can be used for residual stress analysis of glasses, as glass exhibits stress-induced birefringence. In this study, a methodology involving carrier fringes in conjunction with digital photoelasticity is used to quantify the residual stress in float glass. The results are verified by six-step phase-shifting technique (a subset of ten-step phase-shifting method) using an automatic polariscope. Finally, to demonstrate the utility of the proposed method, the residual stress is measured in float glasses of different thicknesses. A method for approximate estimation of residual stress which does not require sophisticated digital image acquisition and processing systems is also reported.     

The effects of residual stress on the mechanical properties of glassy polymers

Residual stresses can have either beneficial or detrimental effects on the mechanical properties of plastics. Manufacturing processes frequently impose residual stresses on plastics. In this study, controlled thermal processes were used to impose surface compressive stresses on polycarbonate beam samples (6.4 by 12.5 by 80 mm). Resistance strain gage and photoelastic techniques were developed to measure the magnitude of these stored stresses. The compressive surface stresses were found to be between 14 MPa (2000 psi) and 31 MPa (4500 psi) and to vary with process method and cooling rate. The mean fatigue life (in bending) of the treated beam samples was found to improve by a factor of 10 over that of untreated samples. The increase in the fatigue life of the treated samples appears to be directly related to the magnitude of the surface compressive residual stress in the samples. The imposed residual stress, as determined by photoelastic measurements, has not appreciably relaxed after 1 year of storage at room temperature.     

Simulation of microstructure development in injection molding of engineering plastics

Mathematical models were developed to predict the various microstructural properties, including birefringece, residual stress, and density distributions, in the freely quenched compression molded samples as well as in the injection molded samples. To model the birefringence distribution in the injection molded samples, the BKZ type integral constitutive equation was employed to account for the nonisothermal stress relaxation, which takes place during the cooling stage of the molding cycle. The predicted birefringence agreed well with the experimental data near the mold walls. The residual stress distribution was modeled by the existing thermoelastic theory. The residual thermal stress distribution in the freely quenched samples was predicted very well by the model. However, the predicted residual thermal stresses in the injection molded samples were much larger than the measured ones. A phenomenological model to predict the density distribution in injection molded sample is proposed by including the effects of both cooling rate and the pressure on the density development. The predicted results agreed well with the experimental data.     

Hot Pressing of Annular Alumina–Zirconia Composites

An analysis is performed to predict the densification during and the state of residual stress after hot pressing of annular alumina/zirconia (3Y-TZP) composites. The objective of the analysis was to study the residual stresses resulting from stress gradients during pressing and those from thermal expansion mismatch during the cooling of the compact from the pressing temperature to room temperature. It is predicted that the residual stresses are affected by the respective densification rates of the core and the annulus, their elastic modulus, and thermal expansion coefficient. For the system analyzed in this study, it is predicted that hot pressing reduces the residual stresses that result from the mismatch in thermal expansion coefficients. This is due in part to the high densification rate and in part to the high elastic modulus of the alumina annulus compared to the zirconia core. For surface compression strengthening, a system where the annulus would have similar elastic modulus but lower densification rate and lower thermal expansion coefficient than the core would be more beneficial.     

Residual Stress Distribution and Characterization on Multi‐Curved Armor Tiles

Residual stresses were measured on numerous multi‐curved, ballistic tiles made from either silicon carbide or boron carbide. Residual stresses were measured at 155 locations to determine what affect parameters such as material, material processing, tile geometry, and manufacturer had on residual stress type and magnitude. 23% of data points had tensile residual stress. The highest residual stresses were measured in tiles with either the largest surface area or smallest plate thickness. Higher stresses were measured in silicon carbide tiles compared with boron carbide tiles. Residual stresses in tiles consolidated by hot pressing measured on average 10 MPa higher than those by pressureless sintering.     

Apparent volumetric shrinkage study of RTM6 resin during the curing process and its effect on the residual stresses in a composite

A comprehensive characterization of the volumetric shrinkage of a commercially important aerospace resin (RTM6) during the various stages of the curing process was studied. The apparent volumetric shrinkage, evaluated from density measurements at room temperature, was correlated with the progress of epoxide conversion. During the entire curing process, the apparent volume shrinkage was found to be less than 3% and occurred before vitrification. A slight re‐expansion of the resin, attributed to self‐antiplasticization effects, was observed during postcuring at 180°C. It was concluded that residual stresses were not generated due to chemical cross‐linking during curing but rather from thermal contraction occurring during the cooling stage after cure. A photo‐elastic method was used to characterize residual stresses during cooling in a deliberately engineered resin rich hole of a carbon fiber/RTM6 composite. The residual stress was found to reach approximately 28 MPa, which is in good agreement with the value calculated from the shrinkage and elastic moduli. It is proposed that this simple method can be provide insights useful to the design and materials selection processes by measuring and localizing residual stresses from resin during curing and or thermal cycling. POLYM. ENG. SCI., 2012. © 2011 Society of Plastics Engineers     

Stress and Volume Relaxation in Annealing Flat Glass

Laboratory simulation of the industrial process of annealing sheet glass has yielded data on the genesis of stresses in initially stress-free glass. The experimental results differed from expectations based on classical annealing theory in that stresses began to develop in the annealing range even when the glass was being cooled at a constant rate, i.e. even in the absence of any changes of temperature gradients within the glass. Typically, these stresses account for 40% of the total residual stress in glass annealed according to a linear schedule. The remaining 60% are the well-known thermoelastic stresses that arise later in the annealing process from the decay of temperature gradients in the glass. The stresses observed to arise in glass as it is being cooled at a constant rate are attributed to volume relaxation effects which, in parts of the annealing range, generate stresses rapidly enough that they are not dissipated by stress relaxation. A mathematical model of annealing is proposed that takes account of both stress and structural relaxation. The model fits the experimentally observed evolution of stresses during linear cooling. It also suggests that (with the activation energies of stress and structural relaxation about the same) the actual rate, at any given temperature, of structural relaxation is about 4 times lower than that of stress relaxation.     

Thermal residual stresses in bilayered,trilayered and graded dental ceramics

Layered ceramic systems are usually hit by residual thermal stresses created during cooling from high processing temperature. The purpose of this study was to determine the thermal residual stresses at different ceramic multi-layered systems and evaluate their influence on the bending stress distribution. Finite elements method was used to evaluate the residual stresses in zirconia-porcelain and alumina-porcelain multi-layered discs and to simulate the ‘piston-on-ring’ test. Temperature-dependent material properties were used. Three different multi-layered designs were simulated: a conventional bilayered design; a trilayered design, with an intermediate composite layer with constant composition; and a graded design, with an intermediate layer with gradation of properties. Parameters such as the interlayer thickness and composition profiles were varied in the study. Alumina-porcelain discs present smaller residual stress than the zirconia-porcelain discs, regardless of the type of design. The homogeneous interlayer can yield a reduction of ~40% in thermal stress relative to bilayered systems. Thinner interlayers favoured the formation of lower thermal stresses. The graded discs showed the lowest thermal stresses for a gradation profile given by power law function with p=2. The bending stresses were significantly affected by the thermal stresses in the discs. The risk of failure for all-ceramic dental restorative systems can be significantly reduced by using trilayered systems (homogenous or graded interlayer) with the proper design.     

Constrained Densification of Alumina/Zirconia Hybrid Laminates, II: Viscoelastic Stress Computation

To analyze the inhibited densification during sintering and differential shrinkage during cooling of Al₂O₃/ZrO₂symmetric and asymmetric laminates, viscoelastic formulations, in which the viscosity and elastic modulus vary with time, have been developed. The viscoelastic mismatch stresses have been numerically computed over the entire processing cycle, including the heating period, the isothermal period, and the cooling period. The viscosity and free sintering rates that are needed for stress computation have been obtained by modifying the parameters that are measured for a normal isotropic densifying compact using cyclic loading dilatometry. The modification is based on the available sintering models to account for the effect of strain history on compact viscosity and sintering rates. The stress calculation shows that, with the exception of the initial heating period, the viscoelastic stress is identical to the viscous stress that is calculated solely from the strain rate mismatch. Sintering damage in the laminates is shown to occur during densification under conditions where the differential sintering stress is smaller than the intrinsic sintering pressure. The magnitude of residual stress in hybrid laminates on cooling is dependent on the cooling rate, and slower cooling rates are capable of almost completely relaxing the expansion mismatch stress at temperatures of >1200°C.     

Assessment of residual stresses during cure and cooling of epoxy resins

A new stress monitoring technique, a stress-tracking device, is described here. It has been used to study some important properties of epoxy resin. Residual stresses, including a curing shrinkage stress and a cooling shrinkage stress, were measured automatically and continuously during curing and cooling. Simultaneously, information such as an apparent gelation time and glass transition temperature were obtained directly during the experiment. These epoxy resin properties were related to the extent of cure. Varying cure temperature produced changes of cure behavior, which resulted in different residual stresses.     

Stress birefringence patterns in molten polymers during the mold-filling and cooling process

An experimental study has been carried out to better understand the phenomenon of stress buildup during the mold-filling process in the injection molding operation. For the study, a rectangular mold with two glass windows was constructed, so that stress birefringence patterns of molten polymers flowing into the mold could be photographed with the aid of a polariscope. As a feeding system, a 1-in. extruder was used attached to the mold with a 2-ft length of stainless steel tubing having a relief valve. In this way, the injection pressure (and injection velocity) was carefully controlled to ensure that the glass windows would not be damaged. The development of stress birefringence patterns during the mold-filling process was recorded on a movie film. It was observed that, in isothermal operation, when flow stopped after the mold was filled, stresses relaxed immediately because of the very slow cooling of the mold by ambient air. However, it was observed that, as cooling proceeded, stresses were gradually built up again in the mold. It was possible, therefore, to determine the residual stress in the mold, which originates from the cooling process alone.     

Residual Stresses in Alumina/Zirconia Composites: Effect of Cooling Rate and Grain Size

Alumina/zirconia composites with various compositions at the zirconia-rich part of the phase diagram have been prepared with various grain sizes of the starting alumina powders. After firing under identical conditions, the pellets have been cooled systematically, changing the cooling rates from 0.5 to 8000 K/min. Subsequently, the residual stresses in alumina have been determined by monitoring the frequency shifts of the R ₂ luminescence line of alumina (14 430 cm⁻¹). The data indicate that the stress in alumina is compressive in all cases, with increasing absolute values of the stress with decreasing alumina content. Within the same composition, the residual stress as a function of the cooling rate presents a minimum for values between 10 and 100 K/min, with no clear dependence on the alumina or zirconia grain size. An interpretation of the experimental data in terms of a Coble-type diffusional relaxation applies for intermediate cooling rates (from 10 to 800 K/min), but it fails to account for the large stresses at low cooling rates. The width of the stress distribution is narrow (∼150 MPa) and constant for all compositions and grain sizes at low cooling rates, but it increases for cooling rates >10 K/min, depending on the grain size but not on the composition. For fast cooling rates, a correlation is found when reporting the average width of the stress distribution as function of the average sintered grain-size distribution of alumina. Overall, zirconia grain size seems to influence the average stress, whereas alumina grain size determines the stress distribution.     

A unified K-BKZ model for residual stress analysis of injection molded three-dimensional thin shapes

The flow-induced and thermally induced residual stresses during injection molding of a thin part with complex geometries are predicted. The injection molding precess was considered to consist of a filling and a post-filling stage (packing coupled with cooling). Additionally, the analysis were applied to successive stages of the process. The model takes into account the viscoelasticity of the molding polymer, which has been neglected in most previous works, because of the complexity of its inclusion. A unified K-BKZ viscoelastic constitutive model, capable of modeling both the fluid-rubbery state and the glass state of amorphous polymers, was employed for simulating this problem. For the flow-induced residual stress predictions of the filling stage, a quasi-steady state approximation was employed for each element of the part, for the calculation of stress profile and subsequent stress relaxation after cessation of flowf. Stress calculations were provided for the thermally induced residual stress predictions of the post-filling stage. These explicit calculations led to the results of pressure and temperature distributions of the part during the post-filling stage into the viscoelastic constitutive model. Additionally, the pressure and asymmetric temeprature profiles of the post-filling stage were based on finite element packing analysis coupled with a boundary element cooling analysis of the molding process. Finally, the total residual stress in the part was obtained via superposition of the flow-induced and thermally induced residual stresses. An example is provided to demonstrate the entire concept. The results indicate that thermally induced residual stress is higher than the flow-induced residual stress by one to two orders of magnitude.     

Residual-Stress–Defect-Severity Relationships in Ceramics

Equivalent-sized fracture-origin defects in partially stabilized zirconia ceramics show dissimilar behavior in initiating fracture. It is suggested that the difference of relative defect severity is related to local residual stresses which develop during sintering and cooling and to elastic modulus differences in the case of solid inclusions on external loading. The existence of residual stresses associated with various defect types is demonstrated, and their variation with temperature is explored. The relative severity of α-alumina defects in tetragonal zirconia varies with temperature, and it is suggested that this is associated with matrix compressive stress relaxation. The residual stress associated with agglomerate defects is temperature independent, and no residual stress is associated with pores.     

Residual stresses in alumina–zirconia laminates

Significant residual stresses can arise in hybrid ceramic laminates during the densification and cooling processing cycles. The densification stresses in alumina–zirconia laminates were calculated assuming the layers to be linear viscous with data obtained by cyclic loading dilatometry. These stresses placed the zirconia layers in biaxial tension and even at 1 MPa or less, they were sufficient to cause a type of linear cavitation damage. The methodology was also applied to asymmetric laminates, successfully predicting their observed curling behaviour. Thermal expansion mismatch stresses arise during cooling, again placing the zirconia layers in residual biaxial tension and leading to the formation of transverse (channelling) cracks. The stresses were calculated using both elastic and viscoelastic formulations and were confirmed with indentation measurements. Additions of alumina to the zirconia layers were effective in reducing both sources of residual stress and allowed crack formation during processing to be avoided. Residual stresses were also shown to improve mechanical performance.     

The evolution of residual stresses in thermoplastic bonding to metals

The ability to create strong joints between thermoplastics and metals offers many advantages. Differential properties between the polymer and metal generate residual stresses during cooling. In our study, both amorphous thermoplastic thin films and semi-crystalline thermoplastic thin films are joined to metal strips and the curvature is measured during controlled cooling. A series of five designed experiments uses a fast cooling (30°C/s) and slow cooling (4.5–10°C/min) to create different residual stresses. Experimental evidence shows that the residual stresses begin to develop at 190°C for amorphous Poly Ether Imide (PEI, T_g = 210°C), but at 255°C for semi-crystalline Poly Ether Ether Ketone (PEEK, T_g = 143°C). A mechanics based curvature model, combined with the elasticity and viscoelasticity of thermoplastics, successfully predicts the residual stress development. An elastic behavior is exhibited during the fast cooling (30°C/s), whereas a viscoelastic behavior occurs during slow cooling (4.5°C/min).     

Influence of Surface Residual Stress State on Crack Path Evolution in Polycrystalline Alumina

The residual stress distribution in polycrystalline alumina is estimated by an object-oriented finite element method. By combining the microstructural image, individual grain orientation, and the crystal elastic properties, the residual stress distribution under a plane stress assumption is obtained by an analysis cooling of the sample through 1000°C. Furthermore, the residual stresses associated with grain boundary areas are investigated and discussed in the context of the concomitant influence on the observed crack path.