Themes: Advanced Computational Methods in Fracture 

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.
EXTENDED ABSTRACT

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.
EXTENDED ABSTRACT

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.
EXTENDED ABSTRACT

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
EXTENDED ABSTRACT

RECENT ADVANCEMENTS AND APPLICATIONS IN DEVELOPMENT OF SMART CRACK GROWTH SIMULATION

SMART (Separating, Morphing, Adaptive and Remeshing Technology) is a finite element based crack growth simulation framework[1] recently developed in the ANSYS Mechanical Solver. Crack representation is essential for FE based fracture and crack growth simulation. The ability to control the mesh and ensure mesh quality at remeshing are essential for robust and accurate crack growth prediction. In this paper several examples and benchmarks are presented to demonstrate the effectiveness and validity of the SMART framework for complex crack propagation simulation. We will then present the latest technological advancements in SMART development related to meshing control with special focus on meshing refinement and coarsening, and adaptive crack initiation.
EXTENDED ABSTRACT

ADVANCED CRACK TIP FIELD QUANTIFICATION USING DIGITAL IMAGE CORRELATION, MACHINE LEARNING, AND INTEGRAL EVALUATION [Keynote]

We use higher-order Williams coefficients from full-field displacement data obtained by digital image
correlation (DIC) to approximate complex crack tip fields with simpler expressions. The methodology is
based on invariant path integrals and machine-learned crack detection. We demonstrate the framework for
fatigue crack growth experiments of aluminium alloys and compare the results to matching finite element
simulations.
EXTENDED ABSTRACT

SINGULAR INTEGRAL EQUATION FOR SOLVING COHESIVE CRACK PROBLEM FOR INITIALLY RIGID TRACTION-SEPARATION RELATION

In case of an initially rigid traction-separation cohesive relation, the total potential energy is not differentiable. This makes the use of variational operator over it questionable. Therefore, the accurate application of FEM is mathematically doubtful. The present work bypasses this issue by modelling the cohesive crack problem as a singular integral equation and solving it using Chebyshev polynomials.
EXTENDED ABSTRACT

REDEFINED J-INTEGRAL AND J-INTEGRAL RANGE DELTA-J AS FINITE STRAIN ELASTIC-PLASTIC CRACK PARAMETERS [Keynote]

The summary of applications of redefined three-dimensional J-integral and J-integral range Delta-J are presented in this paper. The redefined fracture parameters were derived with a rigorous consideration on energy dissipation into a small volume in the vicinity of the crack front. It can be seen as a rigorous extension of two-dimensional T_ε^*-integral to three-dimensional problem. The equation formulations are briefly presented in this paper. Then, their applications will be presented in the conference.
EXTENDED ABSTRACT