Soonsung Hong

Extraction of cohesive-zone laws from elastic far-fields of a cohesive crack tip: a field projection method

A solution method of an inverse problem is developed to extract cohesive-zone laws from elastic far-fields surrounding a crack-tip cohesive zone. The solution method is named the “field projection method (FPM).” In the process of developing the method a general form of cohesive-crack-tip fields is obtained and used for eigenfunction expansions of the plane elastic field in a complex variable representation. The closing tractions and the separation-gradients at the cohesive zone are expressed in terms of orthogonal polynomial series expansions of the general-form complex functions. The series expansion forms a set of cohesive-crack-tip eigenfunctions, which is complete and orthogonal in the sense of the interaction J-integral in the far field as well as at the cohesive-zone faces. The coefficients of the eigenfunctions in the J-orthogonal representation are extracted directly, using interaction J-integrals in the far field between the physical field of interest and auxiliary probing fields. The path-independence of the interaction J-integral enables us to identify the cohesive-zone variables, i.e. tractions and separations, and thus the cohesive-zone constitutive laws uniquely from the far-field data. A set of numerical algorithms is developed for the inversion method and the results from numerical experiments suggest that the proposed algorithms are well suited for extracting cohesive-zone laws from the far-field data. The set includes methods to find the position and size of a cohesive zone. Further included are discussions on error analysis and stability of the inversion scheme.

Smaller is Softer : An Inverse Size Effect in a Cast Aluminum Alloy

Abstract The stress–strain curves of A356 cast aluminum alloys exhibit an unusual size effect on flow properties: the finer the microstructure, the lower the tensile flow strength. Tensile tests were carried out on specimens made of an A356 alloy with 7% Si as the main alloying element. The specimens were cast at two cooling rates. For both processing conditions the microstructure within each grain consists of pro-eutectic aluminum dendrites separated by a boundary eutectic region of segregated silicon particles of ≈2–3 μm diameter. The fast cooling rate gives rise to a secondary dendrite arm spacing of approximately 20–30 μm, while the secondary dendrite arm spacing obtained with the slow cooling rate is about 80–100 μm. Discrete dislocation plasticity is used to model the inverse size effect in this alloy. The dislocations are represented as line defects in an elastic solid and dislocation nucleation, annihilation and drag are incorporated through a set of constitutive rules. Obstacles to dislocation motion are randomly distributed in the dendrite and the eutectic regions, but with different densities and strengths. The thickness of the eutectic region is found to be a key parameter in determining the inverse size effect. In addition, the size effect is found to depend on the extent to which dislocation nucleation takes place in the eutectic region.

Identification of Cohesive-Zone Laws from Crack-tip Deformation Fields

A hybrid framework for inverse analysis of crack-tip cohesive zone model was developed to determine cohesive zone laws from full-field measurement of crack-tip fields by combining analytical, experimental and numerical approaches. The framework is based on the analytical solution method developed to extract cohesive-zone laws from elastic far-fields by using eigenfunction expansion of cohesive crack-tip fields and path-independent integrals. Electronic Speckle Patten Interferometry (ESPI) was used to provide crack-tip deformation fields as input data for the inverse analysis. To overcome ill-conditioning of the inverse problem, a global noise reduction algorithm was developed by implementing a PDE-constrained error minimization problem. The analytical, experimental and numerical approaches were combined to extract cohesive zone laws of fracture processes in glassy polymers, so called crazing. The results demonstrated that the inverse analysis framework provided a systematic and rigorous method to obtain cohesive-zone laws from experimental measurements, so that more realistic cohesive zone modeling can be achieved to predict fracture processes in various engineering materials and interfaces.

Extracting Crack-tip Field Parameters in Anisotropic Elastic Solids From Full-field Measurements Using Least-squares Method and Conservation Integrals

This paper presents parameter-estimation methods developed to determine crack-tip field parameters in anisotropic elastic solids from full-field experimental data. The crack-tip field parameters of interest include not only stress intensity factors but also effective crack-tip positions. Two approaches that are based on least-squares method and conservation integrals were presented. In the approach based on the least-squares method, the Stroh representation of anisotropic elasticity was used to determine the coefficients in the asymptotic expansion of crack-tip fields in anisotropic solids. On the other hand, conservation integrals in fracture mechanics, such as J-integral, M-integral, Interaction integrals, were also used to extract the parameters including the effective crack-tip position. Both approaches were employed to analyze crack-tip displacement fields obtained by using Digital Image Correlation technique during translaminar fracture test of a fiber- reinforced polymer matrix composite. The applicability of homogeneous isotropic plane-elasticity models to translaminar fracture processes in laminated composite materials is also discussed.

Validation of large scale simulations of dynamic fracture

A novel integrated approach is developed for a systematic validation of large-scale finite element simulations on dynamic crack propagations along a weak plane [1]. A set of well-controlled experimental scheme is specifically designed to provide accurate input data for the numerical simulations as well as to provide metrics for quantitative comparisons between experimental and numerical results. Dynamic photoelasticity with high-speed photography is used to capture experimental records of dynamic crack propagations along a weak plane and to provide the crack propagation history. In the dynamic experiments, a modified Hopkinson bar setup with a notch-face loading configuration is used to obtain controlled loading conditions for the dynamic fracture problem. Also an inverse-problem approach of cohesive zone model is employed to obtain a realistic cohesive law, i.e. a traction-separation law, of the weak plane, from independently measured crack-tip deformation fields using speckle interferometry technique. The experimentally collected data, the loading conditions and the cohesive law, are considered as input for the finite element simulations [2]. We employ finite-deformation cohesive elements to account for crack initiation and growth in bulk finite-element discretizations of the experimental sample. As it is well know, the cohesive elements introduce an additional material-dependent length-scale into the finite element model. The demand of accurately resolving this length-scale by the finite-element discretization, as required for truly mesh-independent results, may often lead to discretizations containing several millions of elements. We therefore resort to massively parallel computing.