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In this paper, a coupled plasticity-phase field model for ductile fracture is proposed. The Drucker-Prager plasticity model, which have been applied to metals, concrete, polymers, foams, and other pressure-dependent materials, is coupled with the phase field method. The governing equations are determined by a minimization principle that results in balance laws for the coupled displacement-fracture phase field problem. Furthermore, the finite element implementation, discretization and integration algorithms for the proposed model are presented for three-dimensional, plane strain and plane stress states. In addition, to control the influence of the plastic work and its effect on the crack propagation process, a threshold variable is introduced. Using a numerical example, it is demonstrated that a specific length scale and a certain minimum element size is necessary such that the regularized crack surface converges to the sharp crack. The accuracy of the proposed model and integration algorithm is verified by comparing the obtained results with existing experimental data. In addition, the Arcan sample, by means of a special test setup, allows to load a sample at different direction, and thus performing mixed mode fracture investigation using the model.

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Recently, the phase field approach has gained popularity as a versatile tool for simulating crack propagation. The purpose of this study is to employ the capabilities of the phase field method for crack growth modeling in complex structures such as porous media. The phase field method does not need predefined cracks and it can simulate curvilinear crack path. This goal is accomplished by replacing the sharp discontinuities with a scalar damage phase field parameter representing the diffuse crack topology. To simulate brittle fracture in this study, the equations of elastic displacement field and fracture phase field are first introduced. Afterwards, using the weak form of the equations, the staggered solution of the equations is performed. To implement the equations in the finite element method, the Abaqus software with User Element Subroutine (UEL) is used. Given that the bone structure is somehow a porous structure, a representative volume element of the bone is selected for phase field simulation. In order to verify the developed model, the tensile test of the single edge notched specimen has been simulated. Subsequently, crack propagation in a porous media with different porosities under tensile loading was simulated. The simulation results illustrate the capability of the phase field method in predicting crack growth in geometrically complex structures. In addition, the load-carrying capacity or the strength of the porous structure continuously decreases with increasing porosity and noteworthy is that such a strength is suddenly decreased around a critical porosity value.

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The accurate prediction of crack initiation and growth in manufacturing processes is crucial for minimizing production costs and enhancing the reliability of components. This study focuses on integrated experimental investigation and fracture modeling approach for ductile metals, particularly addressing the mechanisms of ductile fracture and shear localization. The importance of establishing robust damage criteria for accurate reliable numerical simulations cannot be denied. Current literature reveals a significant lack of data on shear and ductile fracture criteria for materials like stainless steel alloy 304. To address this gap, a series of experimental tests was conducted to extract the necessary coefficients for these criteria. Various sample geometries were analyzed to investigate the effects of different triaxiality stress states and loading rates on fracture initiation. The triaxiality stress states were chosen within a range of 0.2 to 2 and strain rates were applied at values of 0.02 s^-1, 4.5 s^-1, and 30 s^-1. A set of coefficients for modeling ductile and shear fracture was derived, taking into account the effects of loading rate and orientation. This research not only provides critical coefficients for fracture modeling but also supports the optimization of manufacturing processes in the automotive industry and other sectors, ultimately contributing to improved material performance and component reliability