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

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 expres-sions for determining Weibull material scale parameters and probability of failure for the two-point bending test. The presented solution, tested on Corning (R) Willow (R) 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 (mA or 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.