Statistical Research On Hot-cutting Defect In Al₂O₃ Ceramic Packaging And Its Impact On The Fracture Strength

With desirable mechanical, electrical and chemical properties such as high strength, high electrical resistivity over broad temperature ranges, high dimensional stability and high chemical inertness, alumina ceramic is extensively applied in aerospace, military, power and automotive electronics with severe operating environment and high-reliability-required fields. But the inherent brittleness makes structure sensitive to defects introduced during fabricating, machining and shipping processes, which is testified repeatedly in the observation of the failure originated from the side surface or edges of the ceramic packages. Ceramic substrates or carriers with whether simple shape or complicated structure, their external profiles are formed by hot-cutting process in green state. However, discontinuities or defects generated in this machining process have rarely been noticed. Actually, these defects can’t be healed by the mass flowing and reconstruction in sintering process and eventually reside on the side surface and edges, exposing to external loading directly and provoke disaster in reliability. Thus, characterization and estimation of the newly-discovered hot-cutting defect mean a lot to the quality controlling and reliability improving of the ceramic package manufacturing.Responding of the defect to brittle fracture strongly depends on its shape and size. Optical and scanning electron microscope are employed to observe the morphology of the hot-cutting defect and cracking-like defect on the side surface and tearing-like defect on the edges are found as the hot-cutting defect. Based on Griffith fracture criteria, three-point flexural test is utilized to estimate the hot-cutting defect quantitatively. Considering surface factor, machining factor in green state and wearing factor of the blade, full factorial experiment is designed and variance analysis is conducted to estimate the hot-cutting defect, which reveals the hot-cutting defect is more dangerous and resulting in a remarkable statistically strength decline reached to 50-60 MPa. The chipping and notch defect on the edge is prone to be a tensile failure in green state and as an inherent defect in hot-cutting process, the wearing of blade can only affect the defect generating slightly.Brittle fracture dominated by defect is statistically scattered. In most situations, fracture strength is statistically Weibull distributed, but for the advanced ceramic and micro- and nano- materials, the semi-empirical Weibull model is demonstrated inapplicable theoretically and experimentally. Thus the fracture statistics dominated by this newly-defined defect need to be verified and referred accordingly. Maximum likelihood estimation is used and obvious deviation is found between the observed strength data dominated by hot-cutting defect and Weibull distribution. Kernel density estimation is employed to explore the underlying density shape for this new fracture statistics and a single modal with a slightly right skewness density curve is obtained, which implies the samples may come from gamma or lognormal distributions with the similar shape features. Fitting comparison and chi-square test further verified that lognormal distribution is an appropriate statistical model to describe the fracture dominated by hot-cutting defect. To explore the defect size distribution accordingly, defect models are built and simplified to a formulation connecting the fracture strength and defect size. Based on the strength distribution, the destructive defect size distribution function is deduced and from the probability density curve, the characteristic length of the destructive defect size is achieved, of which the intrinsic defect, the characteristic length is 18-19 um, while the for hot-cutting defect, the characteristic length is 150-160 um.Integration and miniaturization of electronic system not only challenges the design and processing technology but also the reliability estimation of the miniature structure for its capability of loading is no longer the same with the properties tested in laboratory of a specified size. Investigation and inference of the size effect dominated by hot-cutting defect is a practical way to solve the problem. Optical observation reveals the hot-cutting defect itself varies with the specimen size and corresponding characteristic strength fitted by lognormal distribution exhibits no size effect with different specimen size, for a contrast, the characteristic strength governed by intrinsic defect exhibits the size effect based on Weibull model. To explore the mechanism behind the difference, cracking path under the flexural loading is observed and interaction between hot-cutting defect is found, which betrays the weakest-link theory that defect should be sparsely distributed. Single and multiple defect/microcrack model is built and J integral of the crack tip is calculated by FEM to interpret the effect of the defect interaction on fracture statistics. The stress intensity factor at crack tip achieved from J integral shows that bigger size and irregular shape of hot-cutting itself shield the stress from the crack tip and interaction from neighboring defect also shields the stress from the crack tip. Both shielding effects leads to an ascending T curve providing a bigger tolerance of the defect size, which makes the fracture no longer insensitive to the defect size and the strength statistics exhibits a “quasi- brittle” behavior.