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An estimating method, which conveniently and quickly predicts solutions of constraint parameter <inline-formula> <tex-math notation="LaTeX">$A$ </tex-math></inline-formula> in <italic>J-A</italic> two-parameter approach of elastic-plastic fracture mechanics (EPFM), was developed and successfully applied on three-dimensional (3D) cracked structures under both uniaxial and biaxial loading condition. The method (estimate formula) for <inline-formula> <tex-math notation="LaTeX">$A$ </tex-math></inline-formula> value estimate was developed theoretically first. Then, based on the obtained numerical solutions of parameter <inline-formula> <tex-math notation="LaTeX">$A $ </tex-math></inline-formula> from finite element analysis (FEA), the coefficient values of the proposed estimate formula were determined for 3D single edge cracked plate (SECP) structures under both uniaxial and biaxial loading, to estimate solutions of parameter <inline-formula> <tex-math notation="LaTeX">$A$ </tex-math></inline-formula> for 3D SECP. Through comparing predicted parameter <inline-formula> <tex-math notation="LaTeX">$A$ </tex-math></inline-formula> values with their FEA numerical solutions from authors and other researchers, it is validated that the proposed estimating method can be used well to predict <inline-formula> <tex-math notation="LaTeX">$A$ </tex-math></inline-formula> values for thin 3D cracked structures. It enables the application of the EPFM <italic>J-A</italic> two-parameter approach on practical engineering structure analysis and design of sensor and other mechanical systems.

An Estimate Method of EPFM Constraint Parameter in 3D Cracked Structures for Sensor Structure Design