Probability of failure and weibull size-scaling parameters for thin glass subjected to two-point bending

Abstract

The two-point bending test is a valuable test for estimating the strength of the thin and flexible glass/ceramic parts that are increasingly used in next-generation flexible electronics devices. We present closed-form expressions for determining Weibull material scale parameters and probability of failure for the two-point bending test. The presented solution, tested on Corning® Willow® glass samples, eliminates the need for iterative and often time-consuming approaches (e.g., Finite Element Analysis) for estimating scale parameters. Considering the strength-controlling flaw distribution on a surface or inside a volume, the solution assumes that the Weibull modulus (m) and scaling modulus (mAor mV) are distinct quantities to ensure the scale parameter is independent of the applied load. This condition reveals a special relationship between the moduli that is unique to two-point bending given its highly non-uniform state of stress, which contrasts with other uniaxial bending tests (such as three and four-point bending) in which both moduli have the same numerical value.