M-integral based damage criterion for two-dimensional elastic-plastic porous plates: a quantitative assessment framework under configurational mechanics
摘要
Porous plate structures are widely used in aerospace for lightweight and high-performance structural design. Due to the diversity and complexity of internal defects, traditional damage assessment methods based on single cracks or simple defects are no longer sufficient. Developing an efficient damage assessment method for porous plates is of significant importance. This paper proposes an M-integral approach to quantify damage in two-dimensional elastic-plastic plates with porous defects based on configurational mechanics theory. The expression of the M-integral and its establishment as a damage criterion are presented. The critical load and corresponding M-integral values for porous elastic-plastic materials are calculated with the phase field method, leading to the construction of a damage parameter Ψ, which integrates porosity, initial hole area, and the M-integral to characterize the degradation of material strength. The proposed criterion is validated through uniaxial tensile tests on No. 45 steel plate specimens containing periodic arrays of holes. The results demonstrate that the critical load predicted by the Ψ-parameter has an error margin of less than 10% compared to experimental results, and the critical ΨC at fracture shows an approximate independence of the number and spacing of holes. Furthermore, the Ψ value monotonically increases after the material reaches overall yielding, providing a reliable benchmark for damage evolution. This study extends the application of the M-integral to the quantitative damage assessment of porous plates, providing a potential basis for the integrity assessment of engineering porous structures.