DEVELOPMENT AND APPLICATION OF THE HYPERCOMPLEX FINITE ELEMENT METHOD FOR LINEAR AND NONLINEAR ENERGY RELEASE RATE CALCULATIONS [Keynote]

The augmentation of existing finite element codes to use complex and hypercomplex variables and algebras provides an accurate and straightforward method to compute the energy release rate for linear and nonlinear solids. The basic concept is to introduce complex nodes defined by real and imaginary nodes. The real nodes define the geometry and the imaginary nodes define the perturbation to the real mesh. The crack is extended using imaginary coordinates surrounding the crack tip. The solution of the complex system of equations then yields a complex displacement with the imaginary displacement equal to the derivative of the displacement with respect to the crack length. Subsequently, the energy release rate (the derivative of the strain energy with respect to the crack length) can be determined using from the complex strains and stresses. The results indicate that the ERR results are as accurate as the J integral but the method has several advantages: there are no contours to interrogate – only one result is provided, the method works for both linear and nonlinear materials with loading and unloading, unlike the J integral, and no integral formulation must be developed and implemented. Numerical examples demonstrate the accuracy of the method.
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FINITE ELEMENT MODELING FOR PREDICTING OPTIMAL HOLE PROFILE IN A FINITE SQUARE PLATE OF HETEROGENEOUS BRITTLE MATERIAL (WC+CO) UNDER UNIAXIAL COMPRESSION OR UNIAXIAL DISPLACEMENT

The objective of this paper is to develop numerical models to predict and optimize the ratio (D/W) of hole diameter D over plate width W of a square plate with a center hole. The plate is made from tungsten carbide. The geometry of the model was a square plate with a circular hole in the center. FEM simulation was performed for hole diameter to plate width ratio from 0 to 0.71 in terms of fracture strength (Sut or Suc) under uniaxial compression, or uniaxial displacement. SCF values in the simulations showed good fit with analytical values.It is shown that maximum normal tensile stress develops at the upper point along the free edge of vertical hole,and maximum compressive stresses at left and right horizontal points along the free edge of the hole.. The numerical solution of the normal tensile stress distrbution on the “future fracture plane in Mode I” guarantees a certain degree of stability in the crack propagation in heterogeneous brittle materials.This stability, caused the compliance of the plate to remain independent of crack length, and hence
the fracture toughness can be measured by the critical load itself. The results are relevant to the design of inserts cutting tools.
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MECHANICAL MODEL OF SLIDING FRICTION AND THE STUDY OF THE ONSET OF SLIDING FRICTION

Friction widely exists in our daily life and nature, and the onset of sliding friction plays an important role. However, the underlying physical mechanism of this dynamic process is still unclear. This paper will further explore the physical nature of crack like defects. We reduce the experimental configuration to a slider-substrate model, where the slider can be described using thin long beams and the substrate is considered as an elastic half-space. In this way, the relevant displacement and stress field solutions can be obtained by solving Cauchy singular integral equations. The numerical results can well describe the experimental results. By introducing a critical criterion for static dislocation nucleation, the calculated critical forces are in good agreement with those of the sliding precursor. Based on the model, the dynamics of the sliding precursor is further considered. It is found that the strain field caused by the moving dislocation is in good agreement with the strain field caused by the defect in the experiment, and the transient emission process of the interface edge dislocation is similar to the spatio-temporal dynamic behavior observed in the experiment. These works may contribute to further understanding of the mechanism related to sliding friction processes.
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ROLE OF LOCALIZATION LIMITERS AND LENGTH-SCALES IN MESH OBJECTIVE DYNAMIC FRACTURE MODELING

The objective of this work is to critically assess two commonly used localization limiters, viz. the crack band model (CBM) and rate dependent damage (RDD) for continuum scale dynamic fracture predictions. For this purpose, dynamic mode I fracture for an isotropic brittle material is considered under various loading rates and mesh sizes. A scalar damage model is employed, in conjunction with both localization limiters. The analyses reveal that neither of the localization limiters can successfully regularize the solution across all loading rates. Thus, with local damage models, mesh objective prediction of dynamic fracture can be completely ensured only if the mesh size is kept fixed.Role Of Localization Limiters And Lengthscales In Mesh Objective Dynamic Fracture Modeling
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3D FRACTURE MECHANICS ANALYSIS OF THERMOMAGNETOELECTROELASTIC ANISOTROPIC SOLIDS ACCOUNTING FOR CRACK FACE CONTACT WITH FRICTION

Thermal expansion of the material usually causes existing cracks to close, resulting in the requirement to consider contact problems. The latter are complicated since one should consider the contact of crack faces accounting for sliding, friction, and unknown contact area. This study tries to solve this task by development of the 3D boundary element approach with iterative solver, which can determine the contact zone, sliding of crack faces and account for friction between them. Moreover, multifield materials and various thermal, mechanical, electric and magnetic boundary and contact conditions can be considered.
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CYCLIC EFFECTIVE NEAR-FIELD LOADING BASED ON THE DOMAIN INTEGRAL METHOD

This paper presents a modification of the domain integral method for cyclic loading and crack closure to compute the cyclic effective J-Integral as a near-field loading parameter. The path-dependency of the solution is discussed for different reference states of the field quantities in a cycle. It turns out that refering to the crack opening time point the cyclic effective J-Integral is path-independent for a domain outside the active plastic zone. The validity of this procedure is discussed by comparison with a global energy approach and theoretical field solutions for the J-controlled zone.
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A PERIDYNAMIC FATIGUE MODEL BASED ON TWO-PARAMETER REMAINING-LIFE FORMULATION

In this paper, a new two-parameter remaining-life concept is introduced in the development of a peridynamic fatigue model. Based on the proposed remaining-life concept, the R-ratio effect is accounted for in the crack growth simulations by applying two independent controlling parameters of cyclic bond strain and maximum cyclic strain in the peridynamic remaining-life governing equation. The validation of the model is performed by assessment of correlation between predicted and experimental crack growth data for 2024-T3 aluminum alloy at various R-ratio loading conditions. The model predicted results show a good agreement with experimental crack growth data.
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FAST INFERENCE OF CRACK TIP POSITION AND STRESS INTENSITY FACTORS FROM DISPLACEMENT DATA

Fracture prognosis and characterization efforts require knowledge of crack tip position and the configurational driving force acting on the crack. Here, we present an efficient numerical approach to determine these characteristics under a consistent theoretical framework from displacement data. The novel approach utilizes the separable characteristics of the asymptotic linear elastic fracture mechanics model to expedite the search for crack tip position and is particularly useful for noisy displacement data.

The importance of accurately locating crack tip position is assessed when quantifying the crack driving force from observed displacements. The proposed separability approach for quickly inferring crack tip position is introduced, setting the stage for subsequent assessment of the utility of the separability approach. Comparing to the widely-used displacement correlation approach, we examine performance in cases involving bad starting guesses, noise, and non-conformance with the asymptotic linear elastic fracture mechanics model, e.g. inelastic material behavior and finite geometries. We envision our proposed separability method and the associated code that has been made freely available to be of use to those doing experiments (involving digital image correlation) and simulations where the crack tip position is not explicitly defined, e.g. finite elements with damage models and atomistic simulations of crack growth.
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SIMULATING CRACK CLOSURE WITH COHESIVE ZONE ELEMENTS DURING CRACK GROWTH

Closure and the cohesive effect at crack fronts/surfaces play key roles in simulating crack growth. In this paper, fracture analysis method has been coupled with finite element remeshing techniques to automatically insert cohesive zone element on crack surfaces when cracks propagate, and then multiple cohesive zone models are compared and discussed. This feature has been implemented in Ansys Mechanical MAPDL so that customers are capable of accurately analysing crack growth in a more general background.
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