Development of methods and related criteria for the three-dimensional fracture behavior of elastic-plastic materials under mixed mode loading

Fracture mechanics is of critical importance in high-tech and safety-demanding fields such as defense, aerospace, and maritime industries. Studies on the initiation and propagation of cracks in materials used in various fields, such as engineering structures, are conducted through fracture mechanics, a fundamental area of solid mechanics and materials science. In these analyses, the mechanical behaviors of materials are studied to obtain information that is used to predict structural integrity. Using fracture mechanics, mathematical models are developed to estimate the crack propagation rate and the sudden fracture force by calculating the threshold stress intensity factor and fracture toughness at crack tips for brittle materials. For ductile materials, methods such as the J-integral and Crack Tip Opening Displacement (CTOD) are used to characterize the behavior at the crack tip. Materials used in high-tech fields are generally expected to have high strength and toughness. An accurate understanding of the fracture behavior of these materials is crucial for characterizing potential fracture and damage processes, making intensive use of the principles of fracture mechanics. Modern applications of fracture mechanics using numerical analysis methods, such as the finite element method, provide solutions for various crack geometries. This allows for the selection of materials and geometries in the design processes across various fields, leading to optimal designs specific to each application. The literature includes studies that have produced successful predictive models for cracked materials under plane stress, plane strain, and general three-dimensional loading conditions. Some of these studies employ linear-elastic fracture mechanics principles that include small-scale yielding conditions, while others focus on elastic-plastic fracture mechanics. Since many practical engineering structural and machine elements require high toughness and are subjected to mixed-mode loads, existing linear-elastic fracture mechanics principles cannot provide solutions for elements made of ductile materials. Experimental and analysis-focused studies in the field of elastic-plastic fracture mechanics found in the literature predominantly address problems under mode-I loading conditions. Therefore, this study comprehensively examines the fracture behaviors of ductile metallic materials under mixed-mode in-plane and general three-dimensional loadings, containing larger plastic deformation regions beyond small-scale yielding at the crack tip. The study includes experimental and detailed nonlinear analyses of the fracture behaviors of materials under various mixed-mode loading conditions and develops validated fracture criteria and related analysis methods based on the obtained data. In the scope of the thesis, methods commonly used in both linear-elastic fracture mechanics and nonlinear elastic-plastic fracture mechanics applications were examined and their outputs compared. Initially, calculations were performed using the J-integral method, resulting in similar outcomes obtained from different methods for linear-elastic analyses of cracks under plane loading. However, the J-integral only calculates the total energy release rate. Therefore, a specific mode decomposition method is needed for cracks under mixed-mode loading. Since such a study requires a comprehensive partitioning and high-level formulation, a newly adapted version of the virtual crack closure technique (VCCT) for elastic-plastic analyses, with a much simpler and more applicable equation structure, was used in this study. This method allows direct calculation of energy release rates related to different deformation modes at the crack tip for linear-elastic problems without requiring additional mode decomposition work. The adapted VCCT method for elastic-plastic fracture problems is named AFPER (Artificial Fracture Process Energy Rate). To apply the VCCT method, the displacements and reaction forces at the nodes at the crack tip were calculated using ANSYS 12.1 software. These values were then used to calculate the energy release rates for the opening mode (GI), sliding mode (GII), and tearing mode (GIII) using C#. The calculated energy release rate values were compared with the successful results provided by the FCPAS program for linear-elastic fracture mechanics problems. Another comparison involved the total energy release rate values calculated by the J-integral application and the output of the VCCT method. Both methods showed that the values calculated by the VCCT method were consistent with linear-elastic materials with minimal differences. The basic working principle of the VCCT method focuses on calculating the area under the reaction force-displacement curve at the crack tip. This curve is linear for linear-elastic fracture problems, and the area is calculated using the triangle area formula. To adapt the VCCT method for nonlinear elastic-plastic fracture problems, incremental loading steps with nonlinear analyses were performed, and reaction forces and displacements were calculated for each step's relevant nodes. When this curve is divided into steps, the first step forms a triangle, and subsequent steps form trapezoids. The areas formed by each step were calculated separately and summed, calculating the area under the nonlinear reaction force-displacement curve for nonlinear elastic-plastic materials, named the 'artificial fracture process energy rate' (AFPER). The results were compared with some mode-I J-integral studies in the literature, showing that the values were close to each other. Thus, AFPER was determined to be usable for characterizing the fracture loads of ductile materials. However, since variables such as thickness and crack length affect the resistance to fracture and directly impact the AFPER value in ductile materials, additional parameters are needed for a polynomial equation or relationship. Therefore, a new parameter was developed, called the 'artificial recoverable unloading energy rate' (ARUER), based on the assumption of unloading the reaction force-displacement relationship at the final step of the crack linearly to the zero-force and zero-displacement position. Fracture toughness tests were conducted with AL-2024 T351 material with different thicknesses, crack lengths, and mixed-mode loading angles within the thesis study. Finite element models prepared based on the crack lengths and fracture loads obtained from these tests calculated AFPER, ARUER, the plastic zone radius at the crack tip (RP), and Crack Tip Opening Displacement (CTOD) values. Polynomial equations were developed with these four parameters to predict fracture loads, which accurately estimated fracture loads for mode-I and mode-I/II tests within acceptable differences, but failed for problems with mode-III loading. Criterion development studies continued directly with the AFPER/ARUER ratio. In this context, the average of the AFPER/ARUER ratios calculated from mode-I analyses was named the critical AFPER/ARUER ratio. The load direction under which mixed-mode tests are performed is the parameter that most changes the AFPER/ARUER ratio. While AFPER/ARUER values in mode-I analyses are close to each other, values in mode-I/II analyses are also close but distant from the mode-I average value, and values in mode-I/III analyses are close to each other but distant from the mode-I and mode-I/II average values. Regression analyses were performed with mode-I/II and mode-I/III values, aiming to have AFPER/ARUER values close to the mode-I average value in other mode loadings. Independent mode-I/II/III tests' results were examined with the calculated equation, and it was observed that the developed criterion accurately predicted fracture loads for all tests with low and acceptable differences. After confirming that the method could predict fracture loads for Al-2024 within an acceptable range, the next step was to investigate its compatibility with a more ductile material. Therefore, some tests were repeated using Al-5083 H111 material, demonstrating that the method could be correctly used for a more ductile and different material. The AFPER/ARUER method developed for calculating fracture loads of ductile materials was compared with fracture load results obtained using LEFM predictive methods, and the differences were evaluated. Especially for the more ductile Al-5083 tests, fracture loads calculated using LEFM methods showed very high differences and errors when compared with experimental results. On the other hand, experimental fracture loads were predicted within differences of approximately 10% using the AFPER/ARUER method. In the final stage of the thesis, SEM images of the fracture surfaces of specimens made of Al-2024 material were compared with those of Al-7075, a brittle material, and Al-5083, a more ductile material.