The accuracy of an adopted cohesive zone model (CZM) can affect the simulated fracture response significantly. The CZM has been usually obtained using global experimental response, e.g., load versus either crack opening displacement or load-line displacement. Apparently, deduction of a local material property from a global response does not provide full confidence of the adopted model. The difficulties are: (1) fundamentally, stress cannot be measured directly and the cohesive stress distribution is non-uniform; (2) accurate measurement of the full crack profile (crack opening displacement at every point) is experimentally difficult to obtain. An attractive feature of digital image correlation (DIC) is that it allows relatively accurate measurement of the whole displacement field on a flat surface. It has been utilized to measure the mode I traction-separation relation. A hybrid inverse method based on combined use of DIC and finite element method is used in this study to compute the cohesive properties of a ductile adhesive, Devcon Plastic Welder II, and a quasi-brittle plastic, G-10/FR4 Garolite. Fracture tests were conducted on single edge-notched beam specimens (SENB) under four-point bending. A full-field DIC algorithm was employed to compute the smooth and continuous displacement field, which is then used as input to a finite element model for inverse analysis through an optimization procedure. The unknown CZM is constructed using a flexible Bspline without any "a priori" assumption on the shape. The inversely computed CZMs for both materials yield consistent results. Finally, the computed CZMs are verified through fracture simulation, which shows good experimental agreement.

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The cohesive zone model (CZM) is a key technique for finite element (FE) simulation of fracture of quasi-brittle materials; yet its constitutive relationship is usually determined empirically from global measurements. A more convincing way to obtain the cohesive relation is to experimentally determine the relation between crack separation and crack surface traction. Recent developments in experimental mechanics such as photoelasticity and digital image correlation (DIC) enable accurate measurement of whole-field surface displacement. The cohesive stress at the crack surface cannot be measured directly, but may be determined indirectly through the displacement field near the crack surface. An inverse problem thereby is formulated in order to extract the cohesive relation by fully utilizing the measured displacement field. As the focus in this article is to develop a framework to solve the inverse problem effectively, synthetic displacement field data obtained from finite element analysis (FEA) are used. First, by assuming the cohesive relation with a few governing parameters, a direct problem is solved to obtain the complete synthetic displacement field at certain loading levels. The computed displacement field is then assumed known, while the cohesive relation is solved in the inverse problem through the unconstrained, derivative-free Nelder-Mead (N-M) optimization method. Linear and cubic splines with an arbitrary number of control points are used to represent the shape of the CZM. The unconstrained nature of N-M method and the physical validity of the CZM shape are guaranteed by introducing barrier terms. Comprehensive numerical tests are carried out to investigate the sensitivity of the inverse procedure to experimental errors. The results show that even at a high level of experimental error, the computed CZM is still well estimated, which demonstrates the practical usefulness of the proposed method. The technique introduced in this work can be generalized to compute other internal or boundary stresses from the whole displacement field using the FE method.

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