Strain-Rate-Dependent Yield Criteria for Progressive Failure Analysis of Composite Laminates Based on the Northwestern Failure Theory J.D. Schaefer 1 & I.M. Daniel 2 Received: 9 July 2016 /Accepted: 7 December 2017 # Society for Experimental Mechanics 2018 Abstract The strain-rate-dependent failure of a fiber-reinforced toughened-matrix composite (IM7/8552) was experimentally characterized over the range of quasi-static (10 -4 s -1 ) to dynamic (10 3 s -1 ) strain rates by testing off-axis lamina and angle-ply laminate specimens. A progressive failure framework was proposed to describe the matrix-dominated transition from linear elastic to non-linear material behavior as determined from the experimentally measured stress-strain material response, and the Northwestern Failure Theory was adapted to provide a set of apparent yield criteria for predicting the matrix-dominated yielding of composites using the lamina-based transverse tension (F 2t y ), transverse compression (F 2c y ), and in-plane shear (F 6 y ) yield strengths. The underlying theory was validated by determining the applicability of the new damage-mode-based yield criteria. Starting with the lamina, the proposed criteria accurately predicted the matrix-dominated yielding. Angle-ply laminates were then investigated to isolate the matrix-dominated laminate behavior based on fiber orientation, and the predictions were found to be in superior agreement with the experimental results compared to the classical failure theories. The results indicate the potential of using the Northwestern Yield and Failure Criteria to provide the predictive baseline for damage propagation from yield to ultimate lamina failure in composite laminates. Keywords Damage mechanics . Lamination theory . Polymer-matrix composites . Non-linear behavior . Progressive damage analysis Introduction Composite failure at the structural scale is designed to be a controlled process comprised of scale-relevant phenomena. Proper implementation of computational models for predicting damage initiation and propagation to ultimate fail- ure for the various (and interacting) matrix and fiber- dominated mechanisms must be completed with an under- standing of the direct model outputs to be correlated with experiments. Furthermore, effective model validation is only achieved when the approach is demonstrated to accurately predict the damage phenomena at multiple levels of the com- ponent hierarchy [1]. While numerous capabilities exist for modeling fiber- dominated material behavior, it is increasingly clear that the application of classical approaches for predicting matrix dam- age in composite laminates remains a challenge [2]. The in- ability of classical theories to accurately predict ultimate lam- ina failure (two-piece) is a critical concern for numerical anal- ysis which requires a fundamental criteria for predicting em- bedded ply failure in complex composite laminates (i.e. pro- gressive failure). It is proposed that any investigation of pro- gressive ply failure in composite laminates first accurately predict in-situ layer failure initiation so that the damage prop- agation models may be effectively implemented. In light of this ‘progressive damage and failure’ frame- work, it is critical to determine not only when a lamina or laminate fails, but when it begins to fail (e.g. when first dam- age occurs). In the current work, matrix yielding is defined as the initiation of the failure process in composite laminates as experimentally measured from the characterized stress-strain curves for off-axis lamina and angle-ply laminate specimens. Macroscopically, the yield point is the point at which the * J.D. Schaefer joseph.d.schaefer@boeing.com I.M. Daniel imdaniel@northwestern.edu 1 The Boeing Company, 6300 James S McDonnell Blvd, Berkeley, MO 63134, USA 2 Northwestern University, 2137 Tech Drive, Evanston, IL 60208-3020, USA Experimental Mechanics https://doi.org/10.1007/s11340-017-0366-z