In situ observations of cracking in constrained sintering

In this paper, we examine the long-standing problem of cracking during constrained sintering of a powder aggregate. Using binder jet 3D printing, we prepare ceramic green bodies in the form of center-notched panels, then use in situ imaging to observe how cracks nucleate and grow from the notch as the material sinters under restraint. Quantitative image analysis allows us to identify important characteristics of the sinter-cracking process, indicating a framework for analyzing the problem and developing methods for avoiding it, including representation of sinter-cracking as a creep crack growth process, use of fracture mechanics parameters to design specimen geometries that do not exceed critical stress intensities, and the possibility of exploiting the inherently ductile nature of sinter-cracking to mitigate damage.     

Constrained Sintering of Silver Circuit Paste

Densification kinetics and stress development during constrained sintering of a silver film on a rigid silicon substrate have been studied. Compared with free sintering, the sintering of constrained silver film exhibits a much lower densification and slower densification kinetics. The densification-controlled mechanism changes from fast grain-boundary diffusion kinetics for free sintering to slow lattice diffusion kinetics for constrained sintering. The in-plane tensile stress developed during constrained sintering of silver film, measured using a noncontact laser-scanning optical system, increases rapidly to a maximum level of 1.0–1.5 MPa initially, gradually decreases, and then becomes constant at 0.8–1.0 MPa. The maximum stress observed increases with increasing sintering temperature as a result of the faster densification rate. It is believed that the retardation of densification kinetics of constrained silver film is caused by a change in densification mechanism and the existence of in-plane tensile stress.     

Crack Growth and Damage in Constrained Sintering Films

The constrained sintering of films on substrates leads to a reduction in densification rate and may lead to processing flaws. This paper reports on a study of damage and cracking in sintering films, with particular emphasis on the growth of preexisting cracks. Experiments have been conducted with glass and polycrystalline Al₂O₃ films on various substrates. The effect of important variables (viz., film thickness, crack length, and friction with the substrate) on crack growth is reported. The experiments with glass films show that cracking occurs above a critical film thickness which is in good quantitative agreement with a recent analysis for this problem. In the case of Al₂O₃ films, we observe a diffuse damage zone ahead of cracks. Crack growth occurs by the coalescence of microcracks with each other and with the main crack. Some possible reasons for this difference between the glass and Al₂O₃ films are presented. As a model for diffuse damage, the stability of a sintering film under spatial variations in constitutive parameters is analyzed. It is shown that the film is unstable to small perturbations only in the early stages of densification, and that for viscous sintering the films are usually kinetically stable.     

Fatigue of Yttria-Stabilized Zirconia: II, Crack Propagation, Fatigue Striations, and Short-Crack Behavior

Fatigue crack propagation in 3Y-TZP was investigated using controlled surface flaws. A unique growth law strongly dependent on the maximum stress intensity factor and quadratically dependent on the amplitude of the range of stress intensity factor was established. This growth law was found to apply for both surface flaws and internal flaws and could be used to predict fatigue lifetime. The presence of residual stress altered the growth mechanics so that an inverse growth rate dependence on the applied stress, reminiscent of the so-called "short-crack behavior," was manifested. Fatigue striations resulting from alternate overload fracture and fatigue fracture during stress cycling were observed. The appearance of striations varied with the R ratio and was very sensitive to the loading condition and crack geometry.     

Modelling of elimination of strength-limiting defects by pressure-assisted sintering at low stress levels

The structural reliability of sintered products depends on large defects introduced during powder processing, which cannot be removed by pressureless sintering. Here, we present a model how a large single ellipsoidal void is deformed, and finally disappears by pressure-assisted sintering. Taya-Seidel’s model is applied to predict the shrinkage of a large void in a compressible linear viscous material by using bulk viscosity, shear viscosity, and sintering stress that are determined experimentally for sintering of alumina powder at low stress levels. The application of mechanical stress promotes the densification rate. Its effect is maximum for hot isostatic pressing (HIP) and minimum for sinter forging. The effect is intermediate for hot pressing (HP) and spark plasma sintering (SPS), because the hydrostatic component of stress varies with densification. While a crack-like defect can be removed during densification, a spherical void must be eliminated by shear deformation in the final stage during dwell time.     

Sintering Stress of Nonlinear Viscous Materials

An analytical model for the sintering stress of materials characterized by a nonlinear viscous behavior during densification is proposed. The growing applications in the field of nanosized powders processing (in particular, consolidation of high surface area components used in supercapacitors, rechargeable batteries, gas absorbers) have renewed the interest in this fundamental parameter of sintering science, because of the sintering stress’ characteristic inverse proportionality with respect to the powder particles radius. This increase in the magnitude of the sintering stress is also responsible for power‐law creep being the mechanism that underlies densification even without the application of any additional external load, and therefore for a nonlinear viscous behavior of the solid material. The analytical treatment of problems involving nonlinear viscous materials has traditionally involved complex self‐consistent methods and approximations, unless the local case of an isolated pore embedded in a fully dense skeleton was considered. The paper proposes a simple first‐order iterative method that allows the derivation of both bulk modulus and sintering stress of a material containing an arbitrary amount of pores, as functions of porosity and of the material's nonlinearity parameter, namely strain rate sensitivity. An expression for densification kinetics is also obtained and compared with experimental data.     

Stress Required to Densify a Low-Fire NiCuZn Ferrite Under Constrained Sintering

The effect of uniaxial stress on the densification behavior of a low-fire NiCuZn ferrite during constrained sintering of a multilayer structure of a ferrite tape and a pure alumina tape has been investigated. Compared with free sintering, the densification of ferrite becomes significantly reduced and slowed down under pressure-less constrained sintering. To enhance the constrained densification of ferrite in the temperature range required for free sintering, uniaxial stress applied in the thickness direction is needed. The required uniaxial stress to densify ferrite under constrained sintering to reach a relative sintered density of >95% decreases from 1100–1300 kPa at 900°C to 250–450 kPa at 1000°C. Moreover, no significant grain growth is found when the ferrite is densified under pressure-assisted constrained sintering.     

Effect of MgO Solute on Microstructure Development in Al2O3

The effect of MgO as a solid-solution additive in the sintering of Al₂O₃ was studied. The separate effects of the additive on densification and grain growth were assessed. Magnesia was found to increase the densification rate during sintering by a factor of 3 through a raising of the diffusion rate. The grain-size dependence of the densification rate indicated control primarily by grain-boundary diffusion. Magnesia also increased the grain growth rate during sintering by a factor of 2.5. The dependence of the grain growth rate on density and grain size suggested a mechanism of surface-diffusion-controlled pore drag. It was argued, therefore, that MgO enhanced grain growth by raising the surface diffusion coefficient. The effect of MgO on the densification rate/grain growth rate ratio was, therefore, found to be minimal and, consequently, MgO did not have a significant effect on the grain size/density trajectory during sintering. The role of MgO in the sintering of alumina was attributed mainly to its ability to lower the grain-boundary mobility.     

Kinetics of Constrained-Film Sintering

Results of shrinkage measurements on constrained and corresponding unconstrained films of materials that densify by viscous flow or solid-state diffusion mechanisms have been presented. Constrained-film shrinkage was measured in situ during sintering using laser reflectance; unconstrained-film shrinkage was measured using scanning electron microscopy (SEM). Data for unconstrained films were fitted to densification kinetics expressions for the operative densification mechanism. Constrained-film shrinkage behavior predicted by the Scherer-Garino model,¹ using expressions that fit data for the unconstrained case, was compared to actual data for the constrained films. Data for the viscous sintering case fit the predictions made by the model well, but data for densification by solid-state diffusion deviated from predicted behavior even when grain growth was accounted for, possibly because of pore growth caused by local densification.     

Segregation-controlled densification and grain growth in rare earth-doped Y2O3

Cation doping of Y₂O₃ is an established approach for tailoring densification and grain growth during sintering. However, the segregation of doped cations to the grain boundary and their impact on processing are still not completely understood. Segregation can be driven by electrostatic effects due to charge mismatch with the host lattice or elastic effects induced by ion size mismatch. While segregation is caused by thermodynamics, it impacts diffusion and the kinetics of grain boundaries during densification and microstructure evolution. In this study, we utilize two isovalent dopants (La³⁺ and Gd³⁺), that is we focus on the elastic component of segregation. We investigate the densification as well as the grain growth kinetics of both doped and undoped Y₂O₃ during field-assisted sintering/spark plasma sintering (FAST/SPS). While Gd³⁺ is showing no significant effect on densification, La³⁺ resulted in a strongly reduced sintering activity. Furthermore, the analysis of the grain growth behavior during sintering and on predensified samples revealed a decrease in the grain growth coefficient, with La³⁺ having the strongest impact. The structure and chemistry at the grain boundary were observed by aberration-corrected TEM. While no structural change was caused by doping, the chemical analysis showed a strong segregation of La³⁺ to the grain boundary, which could not be observed for Gd³⁺. The results indicate that segregated La³⁺ causes a drastic decrease in grain boundary migration rates through solute drag as well as much slower sintering kinetics, likely caused by a decrease in the grain boundary self-diffusion due to segregation. This study further underlines the importance of the elastic contribution to cation segregation and establishes a clear relationship to grain growth and sintering kinetics, which are both decreased by segregation.     

The Effect of Applied Stress on the Densification of a Low-Temperature Cofired Ceramic-Filled Glass System Under Constrained Sintering

The effect of uniaxial stress on the mechanical response and densification behavior of a low-fire borosilicate glass (BSG)+alumina system during constrained sintering of a multilayer BSG+alumina/alumina laminate has been investigated. Compared with free sintering, the pressure-less constrained sintering of BSG+alumina exhibits poorer densification, and larger porous bulk viscosity at a given temperature. This is caused by the in-plane tensile stress and anisotropic development generated in the transverse directions of the laminate during constrained sintering. The applied uniaxial stress required in the thickness direction to densify BSG+alumina under constrained sintering varies in the range of 50–400 kPa at 700°–800°C. The above results are in agreement with those calculated using the viscous analogy for the constitutive relationships of a porous sintering compact.     

氧化锆/氧化铝复相陶瓷显微组织缺陷分析

针对5Y-ZrO2/Al2O3复相陶瓷出现的晶粒异常长大和晶粒开裂问题展开研究。以ZrO2和Al2O3为主要原料,采用常压烧结工艺制备陶瓷样品,利用SEM观察显微组织。分析表明:MgO对抑制Al2O3晶粒异常长大有重要影响,MgO的加入量应随着Al2O3加入量的变化而改变;烧结温度的改变将导致异常长大的Al2O3晶粒细化。当烧结温度较低时,Al2O3晶粒将在短轴方向逐渐断开成段;当温度较高时,则沿着长轴方向逐渐开裂成条状。ZrO2晶粒的断裂主要与烧结温度有关:在1630℃以上烧结时,出现裂纹并贯穿晶粒;晶粒开裂的原因是:烧结温度较高时,陶瓷中形成了t-ZrO2,在降温过程中大颗粒的t相发生t→m相变,而小颗粒t相则无法变成m相,引起局部体积变化不均匀,从而产生相变应力导致晶粒穿晶断裂。     

A micro-macro correlation of ozone-induced fracture in rubber

Rate of molecular bond rupture is successfully correlated by a Griffith-type energy balance to the strain energy release rate during ozone cracking of rubber. Rate of bond rupture is determined from electron paramagnetic resonance (EPR) measurements. The rate of strain energy release is determined from stress–elongation measurements during stress relaxation, creep, and cyclic loading tests. To compare with macroscopic crack studies, it was assumed that each ruptured bond created a given amount of fracture surface. Numerical agreement could be obtained by assuming each broken bond results in the production of an area of approximately 10^?13 cm². Using the surface energy density determined from stress relaxation tests in an energy balance gives surprisingly accurate predictions of expected behavior in creep and cyclic loading tests. There is a one-to-one correspondence between the rate of crack growth (bond rupture) and rate of energy release from strain and external work in all cases. It is proposed that such correlations give credence to a Griffith-type approach to environmental cracking which it did not have previously.     

Cracking and shape deformation of cylindrical cavities during constrained sintering

During constrained sintering of thin films, in which a cylindrical cavity with axis perpendicular to the substrate has been introduced before sintering, cracks emerge that initiate at the cavity surface. By combining experiments with continuum mechanical and particle based simulations, the fundamental causes and effects of this kind of crack formation are identified. A stress analysis performed by finite element (FEM) simulations matches with the cracking behavior observed in experiments. A comparison of discrete element (DEM) results with experiments shows the applicability of this simulation method to describe the effect of cross-sectional stripe dimensions and cavity diameters on the cracking behavior. Moreover, DEM simulations reveal that hair-line cracks in narrow stripe samples formed during pre-sintering manufacturing steps might be a dominant cause for the observed crack damage in such systems.     

Sintering behavior of 8YSZ-Ni cermet: Comparison between conventional,FST/SPS,and flash sintering

Cermets are ceramic metal composites. The metallic phase in the cermet typically undergoes oxidation during sintering in air. Electric field-assisted sintering processes such as field-assisted sintering technology/spark plasma sintering (FAST/SPS) and flash involves very high heating rates, short processing time and low processing temperature. The main aim of this work was to see if field-assisted sintering techniques can prevent the oxidation of the metallic phase in the cermet. Sintering behavior of 8YSZ-5 wt.% Ni cermet was studied by three different techniques namely; conventional sintering, FAST/SPS and flash sintering. Phases and microstructure were analyzed through X-ray diffraction and scanning electron microscopy, respectively. Temperature and time required for sintering the samples via FAST/SPS and flash sintering was significantly lower than that during conventional sintering. In addition, we found limited grain growth during FAST/SPS and flash sintering. During conventional sintering in reducing atmosphere (Ar and vacuum), Ni particles retained their elemental state, however the extent of densification was poor in the cermet. FAST/SPS in argon and vacuum resulted in almost complete densification (relative density > 97%) and Ni particles were retained in their elemental state in the cermet. During flash sintering in air, the samples sintered to a high densification (relative density ∼98%), however, Ni particles were completely oxidized.     

Effect of Interface Structure on the Microstructural Evolution of Ceramics

The interface atomic structure was proposed to have a critical effect on microstructure evolution during sintering of ceramic materials. In liquid-phase sintering, spherical grains show normal grain growth behavior without exception, while angular grains often grow abnormally. The coarsening process of spherical grains with a disordered or rough interface atomic structure is diffusion-controlled, because there is little energy barrier for atomic attachments. On the other hand, kink-generating sources such as screw dislocations or two-dimensional (2-D) nuclei are required for angular grains having an ordered or singular interface structure. Coarsening of angular grains based on a 2-D nucleation mechanism could explain the abnormal grain growth behavior. It was also proposed that a densification process is closely related to the interface atomic structure. Enhanced densification by carefully chosen additives during solid state sintering was explained in terms of the grain-boundary structural transition from an ordered to a disordered open structure.     

Simulation of the Stress-Assisted Densification Behavior of a Powder Compact: Effect of Constitutive Laws

The densification of powders with linear and nonlinear viscous behavior (Scherer and Riedel models) and with power-law-deformation (Khun–McMeeking) behavior was studied under hot pressing and sintering forging conditions. Several numerical experiments, designated cases in this work, were performed to study the effect of (i) the uniaxial stress exerted by the piston and (ii) the rate of the uniaxial stress. The stress state was calculated using the finite-element program ANSYS for each case. Considering the mesoscopic behavior of the powders, densification rates were obtained. The similarities and differences between predictions from the three constitutive models are highlighted. The relationship between the constitutive behavior and the most effective stress state is one of the focuses of this study. For example, we show that under constant stress loading, hot pressing more effectively promotes densification than sinter forging for constitutive behaviors that do not follow the power-law creep. In general, as expected, the increase of uniaxial applied stress and piston velocity favored densification. However, the increase in densification depends strongly on the constitutive law.     

Microstructural Development during Sintering of Lithium Fluoride

Measurements are reported of the influences of temperature, green density, and pore network breakup on the densification, grain growth, and pore volume distribution in LiF compacts. As long as most of the pore volume remained open to the compact perimeter, the ratio of the rate of densification to the rate of grain growth was higher than that sometimes reported for copper or typical oxides. Plots of the logarithm of densification rates versus sintered density for LiF are approximately linear during intermediate-stage sintering, like those for some oxides. But the plots for LiF are unlike those of the oxides in that, for LiF, densification rates measured at different temperatures converge near the density at which half the pore volume is isolated from Hg intrusion. Calculations suggest that further densification of the LiF compacts is blocked because air trapped in isolated pores becomes sufficiently compressed to balance the sintering stress.     

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.