Evaluation of indentation fracture toughness for brittle materials based on the cohesive zone finite element method

Finite element method was used to analyze the three-point bend experimental data of A533B-1 pressure vessel steel obtained by Sherry, Lidbury, and Beardsmore [1] from −160 to −45 °C within the ductile-brittle transition regime. As many researchers have shown, the failure stress (σf) of the material could be approximated as a constant. The characteristic length, or the critical distance (rc) from the crack tip, at which σf is reached, is shown to be temperature dependent based on the crack tip stress field calculated by the finite element method. With the J-A2 two-parameter constraint theory in fracture mechanics, the fracture toughness (JC or KJC) can be expressed as a function of the constraint level (A2) and the critical distance rc. This relationship is used to predict the fracture toughness of A533B-1 in the ductile-brittle transition regime with a constant σf and a set of temperature-dependent rc. It can be shown that the prediction agrees well with the test data for wide range of constraint levels from shallow cracks (a/W = 0.075) to deep cracks (a/W = 0.5), where a is the crack length and W is the specimen width.

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Modelling of triaxial fracture processes in heterogeneous quasi-brittle materials using the Embedded Finite Element Method (E-FEM)

10.31224/osf.io/ecv73 ◽

2021 ◽

Author(s):

Alejandro Ortega Laborin ◽

Yann MALECOT ◽

Emmanuel ROUBIN ◽

Laurent DAUDEVILLE

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Spherical Inclusion ◽

Brittle Materials ◽

Three Dimensions ◽

Strong Discontinuity ◽

Homogeneous Material ◽

Fem Model ◽

Fracture Processes ◽

Element Method

This paper studies the use of the Embedded Finite Element Method (E-FEM) for the numerical modelling of triaxial fracture processes in non-homogeneous quasi-brittle materials. The E-FEM framework used in this study combines two kinematics enhancements: a weak discontinuity allowing the model to account for material heterogeneities and a strong discontinuity allowing the model to represent local fractures. The strong discontinuity features enriched fracture kinematics that allow the modelling of all typical fracture modes in three dimensions. A brief review is done of past work using similar enriched finite element frameworks to approach this problem. The work continues by establishing the theoretical basis of each kind of discontinuity formulation and their superposition through the Hu-Washizu variational principle. Afterwards, two groups of simulations have been done for discussing the performance of this combined E-FEM model: homogeneous simulations and simple heterogeneous simulations. Simple homogeneous material simulations aim to test the capabilities of the strong discontinuity model featuring full 3-D kinematics. Simple heterogeneous simulations show numerical applications of the model to the problem of a single spherical inclusion embedded into a homogeneous matrix. Comparisons will be made with another E-FEM model considering a single local fracture mode approach to discuss the differences on the representation of fracture physics under all explored conditions. A concluding statement is made on the benefits and complications identified for the E-FEM framework in this kind of applications.

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