Porosity in sintered materials negatively affects its fatigue properties. In investigating its influence, the application of numerical simulations reduces experimental testing, but they are ...computationally very expensive. In this work, the application of a relatively simple numerical phase-field (PF) model for fatigue fracture is proposed for estimation of the fatigue life of sintered steels by analysis of microcrack evolution. A model for brittle fracture and a new cycle skipping algorithm are used to reduce computational costs. A multiphase sintered steel, consisting of bainite and ferrite, is examined. Detailed finite element models of the microstructure are generated from high-resolution metallography images. Microstructural elastic material parameters are obtained using instrumented indentation, while fracture model parameters are estimated from experimental S-N curves. Numerical results obtained for monotonous and fatigue fracture are compared with data from experimental measurements. The proposed methodology is able to capture some important fracture phenomena in the considered material, such as the initiation of the first damage in the microstructure, the forming of larger cracks at the macroscopic level, and the total life in a high cycle fatigue regime. However, due to the adopted simplifications, the model is not suitable for predicting accurate and realistic crack patterns of microcracks.
Two mixed meshless collocation methods for solving problems by considering a linear gradient elasticity theory of the Helmholtz type are proposed. The solution process is facilitated by employing ...operator-split procedures, splitting the original 4th-order problem into two uncoupled second-order sub-problems, which are then solved in a staggered manner by applying the mixed meshless local Petrov–Galerkin collocation strategy. Thereby, identical nodal pattern is used for the discretization of both lower-order problems, while the approximation of all unknown field variables is performed by applying the Moving Least Squares functions with interpolatory conditions. The performance of the derived methods is tested by some suitable numerical examples, dealing with elasticity problems that are often treated by gradient theories. Therein, it is demonstrated that both proposed methods are able to capture the size effect and that the strain-based method is able to produce the non-singular strain field around the crack tip, similar to the nonlocal elasticity approach of Eringen. It has been found out that the obtained results agree well with available analytical and numerical solutions.
This research presents a novel approach to modeling fracture propagation using a discrete lattice element model with embedded strong discontinuities. The focus is on enhancing the linear elastic ...response within the model followed by propagation of fractures until total failure. To achieve this, a generalized beam lattice element with an embedded strong discontinuity based on the kinematics of a rigid-body spring model is formulated. The linear elastic regime is refined by correcting the stress tensor at nodes within the domain based on the internal forces present in lattice elements, which is achieved by introducing fictitious forces into the standard internal force vectors to predict the right elastic response of the model related to Poisson’s effect. Upon initiation of the first fractures, the procedure for the computation of the fictitious stress tensor is terminated, and the embedded strong discontinuities are activated in the lattice elements for obtaining an objective fracture and failure response. This transition ensures a shift from the elastic phase to the fracture propagation phase, enhancing the predictive capabilities in capturing the full fracture processes.
The present study deals with the influence of residual stresses induced by the buried-arc welding on the crack behavior in two butt-welded 20 mm thick plates. The following steps were undertaken: the ...thermo-mechanical simulation of the welding process, the mapping of stress results from a finite element (FE) mesh used for the welding simulation to a new FE mesh with a crack, the stress balancing, and the stress intensity factor (SIF) calculation. The FE and weight function (WF) methods were used to investigate the SIFs at the deepest point of semi-elliptical surface cracks with different geometries, orientations, and positions in relation to the weld line. In the case of cracks perpendicular to the weld line, the FE and WF results showed a good agreement for smaller cracks, while deviation between the results increases with the size of the crack. Considering the SIF solutions for the cracks of arbitrary orientation, it was observed that for some cases, the SIF value for mode III of crack opening can be of significant influence.
In this paper, a 3D phase-field model for brittle fracture is applied for analyzing the complex fracture patterns appearing during the Vickers indentation of fused silica. Although recent phase-field ...models for the fracture caused by the indentation loading have been verified by some simpler academic axis-symmetric examples, a proper validation of such models is still missing. In addition, heavy computational costs, and a complicated compression stress field under the indenter, which demands different energy decompositions, have been identified as the most important impediments for the successful application of the phase-field method for such problems. An adaptive strategy is utilized for reducing the computational costs, and some modifications are introduced, which enable an accurate simulation of the Vickers indentation fracture. Here, the fracture initiation ring outside the contact zone is detected by using different energy decompositions, and the dominant cone-crack formation under the Vickers indenter is observed. Different contact conditions are investigated. The proposed model is validated by experimental measurements, and a quantitative and qualitative comparison between experimental and numerical results is conducted.
To assess the behaviour of porous materials, it is important to consider the influence of material microstructure. In this study, a multiscale experimental analysis is conducted to investigate the ...influence of micromechanical parameters, such as the material properties of metallic phases and porosity, on the macromechanical properties of a porous sintered steel. At the microlevel, indentation is conducted to identify microphases and metallographic analysis has been used on mesoscale to measure porosity. Tension uniaxial tests have been applied to characterize macro properties. The results of the tests suggest that the macromechanical properties of porous sintered metallic materials might be mostly influenced by the porosity, while at the microlevel no significant variation in the mechanical properties of microphases has been detected in samples with different density, i.e., porosity. In addition, porosity is related to the sintering density experimentally and an empirical expression that relates density and porosity is proposed.
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An efficient mixed meshless computational method based on the Local Petrov–Galerkin approach for analysis of plate and shell structures is presented. A concept of a three-dimensional solid is applied ...allowing the use of complete three-dimensional constitutive equations, and exact shell geometry can be described. Discretization is carried out by using both the moving least square approximation and the polynomial functions. Independent field variables are the strain and stress tensor components expressed in terms of the nodal values, which are then replaced by the nodal displacements by using the independent displacement interpolation. A closed global system of equations with only nodal displacements as unknown variables is derived. The undesired locking phenomena are fully suppressed. The proposed mixed formulation is numerically more efficient than the available meshless fully displacement approach, as demonstrated by the numerical examples.
A mixed meshless local Petrov–Galerkin (MLPG) collocation method is proposed for solving the two-dimensional boundary value problem of heterogeneous structures. The heterogeneous structures are ...defined by partitioning the total material domain into subdomains with different linear-elastic isotropic properties which define homogeneous materials. The discretization and approximation of unknown field variables is done for each homogeneous material independently, therein the interface of the homogeneous materials is discretized with overlapping nodes. For the approximation, the moving least square method with the imposed interpolation condition is utilized. The solution for the entire heterogeneous structure is obtained by enforcing displacement continuity and traction reciprocity conditions at the nodes representing the interface boundary. The accuracy and numerical efficiency of the proposed mixed MLPG collocation method is demonstrated by numerical examples. The obtained results are compared with a standard fully displacement (primal) meshless approach as well as with available analytical and numerical solutions. Excellent agreement of the solutions is exhibited and a more robust, superior and stable modeling of material discontinuity is achieved using the mixed method.
The paper presents meshless methods based on the mixed Meshless Local Petrov-Galerkin approach used for solving linear fourth-order differential equations. In all the methods presented here, the ...primary variable and its derivatives up to the third order are approximated separately. Three different mixed meshless methods are derived by different choices of test and trial functions and are verified using available analytical and reference solutions. The numerical performance of the presented algorithms is demonstrated by several representative numerical examples.
A new mixed meshless approach using the interpolation of both stress and displacement has been proposed for the analysis of plate deformation responses. Kinematic of a three dimensional solid is ...adopted and discretization is performed by nodes located on the upper and lower plate surfaces. Governing equations are derived by employing the local Petrov-Galerkin approach. The approximation of all unknown field variables is carried out by using the B-spline interpolation and the moving least squares functions in the in-plane directions, while linear polynomials are applied in the transversal direction. In order to eliminate the thickness locking effect, the hierarchical quadratic interpolation of the transversal displacement component through the thickness is used. The shear locking effect is efficiently suppressed by the interpolation of the stress field independently from the displacement. The numerical efficiency of the derived algorithm is demonstrated by numerical examples.
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