Fracture mechanics characterization tests for adhesive joints are analyzed and reviewed in order to understand their advantages and disadvantages. Data reduction techniques for analytical methods are summarized to understand the improvements implemented in each test. Numerical approaches are also used complementing tests information. Both linear and non-linear methods to obtain the fracture energy release rate are presented. Pure mode I and mode II tests are described. Simple mixed-mode tests, varying only the specimen geometry, with limited mode-mixity are also presented. Performing a wider mode-mixity range requires sophisticated apparatus that are studied in detail. There is no general agreement about the test suitability for mixed-mode fracture assessment of adhesive joints. A universal test that can easily be performed and give accurate results is essential to optimize the expensive testing at the design stage.

Fracture Mechanics Tests in Adhesively Bonded Joints: A Literature Review

The paper presents a mechanical model of the mixed-mode bending (MMB) test used to assess the mixed-mode interlaminar fracture toughness of composite laminates. The laminated specimen is considered as an assemblage of two sublaminates partly connected by an elastic–brittle interface. The problem is formulated through a set of 36 differential equations, accompanied by suitable boundary conditions. Solution of the problem is achieved by separately considering the two subproblems related to the symmetric and antisymmetric parts of the loads, which for symmetric specimens correspond to fracture modes I and II, respectively. Explicit expressions are determined for the interfacial stresses, internal forces, and displacements.

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An enhanced beam-theory model of the mixed-mode bending (MMB) test—Part I: Literature review and mechanical model

Mixed-mode I/II wood fracture characterization using the mixed-mode bending test

In this work, fatigue/fracture characterization of composite bonded joints is performed using the Single-Leg Bending (SLB) test. The SLB test provides a mixed-mode I + II loading with a fixed mode mixity. Specimens of carbon fibre reinforced epoxy bonded with a ductile epoxy adhesive were tested considering two load levels. The applicability of the Paris-law establishing a relationship between the fatigue crack growth rate and the variation of the energy release rate was analyzed. An equivalent crack method was used to overcome the difficulties associated to crack monitoring during the fatigue tests. Consistent results were obtained for the lower load level, thus proving the adequacy of the SLB test concerning fatigue/fracture characterization of bonded joints.

Mixed-mode I + II fatigue/fracture characterization of composite bonded joints using the Single-Leg Bending test

A new energy based mixed-mode cohesive zone model

Numerical analysis of the MMB test for mixed-mode I/II wood fracture

This work describes the application of end loaded split and single-leg bending tests to the mixed-mode fracture characterization of wood. Experimental tests and numerical validation analyses were performed. A new data reduction scheme based on the crack equivalent concept is proposed. The method overcomes the difficulties inherent to these tests, such as crack length monitoring during propagation and influence of clamping conditions. The single-leg bending test is simpler to execute and provided accurate results. The obtained mixed-mode fracture energy is associated with the pure mode values and the obtained trend point to a linear fracture criterion as a candidate to describe the fracture behavior of the Pinus pinaster Ait. wood.

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Application of the end loaded split and single-leg bending tests to the mixed-mode fracture characterization of wood.

Mixed-mode (I + II) fracture characterization of wood bonded joints

Governing cohesive laws in mixed mode I+II loading of Pinus pinaster Ait. are directly identified by coupling the mixed mode bending test with full-field displacements measured at the crack tip by Digital Image Correlation (DIC). A sequence of mixed mode ratios is studied. The proposed data reduction relies on: (i) the compliance-based beam method for evaluating strain energy release rate; (ii) the local measurement of displacements to compute the crack tip opening displacement; and (iii) an uncoupled approach for the reconstruction of the cohesive laws and its mode I and mode II components. Quantitative parameters are extracted from the set of cohesive laws components in function of the global phase angle. Linear functions were adjusted to reflect the observed trends and the pure modes (I and II) fracture parameters were estimated by extrapolation. Results show that the obtained assessments agree with previous experimental measurements addressing pure modes (I and II) loadings on this wood species, which reveals the appropriateness of the proposed methodology to evaluate the cohesive law under mixed mode loading and its components.

J.M.Q. Oliveira

Papers

Mixed-mode I/II wood fracture characterization using the mixed-mode bending test

Numerical analysis of the MMB test for mixed-mode I/II wood fracture

Application of the end loaded split and single-leg bending tests to the mixed-mode fracture characterization of wood.

Mixed-mode (I + II) fracture characterization of wood bonded joints

Direct Evaluation of Mixed Mode I+II Cohesive Laws of Wood by Coupling MMB Test with DIC.