Erkan Oterkus

Modelling of stress-corrosion cracking by using peridynamics

We present for the first time a numerical multiphysics peridynamic framework for the modelling of adsorbed-hydrogen stress-corrosion cracking (SCC), based on the adsorption-induced decohesion mechanism. The material is modelled at the microscopic scale using microstructural data. First-principle studies available in the literature are used for characterizing the process of intergranular material strength degradation. The model consists of a polycrystalline AISI 4340 high-strength low-alloy (HSLA) thin, pre-cracked steel plate subjected to a constant displacement controlled loading and exposed to an aqueous solution. Different values of stress intensity factor (SIF) are considered, and the resulting crack propagation speed and branching behaviour are found to be in good agreement with experimental results available in the literature.

Fatigue failure model with peridynamic theory

This study presents a methodology to predict the fatigue failure of materials due to cyclic loading within the realm of peridynamic theory. This approach incorporates material failure intrinsically without the need for external crack growth criteria and post-processing. Failure occurs when and where it is energetically favorable. Fatigue life prediction is a natural extension of crack initiation and growth while allowing material degradation. The present approach focuses on the crack growth phase of fatigue life rather than initiation. During the crack growth phase, material degrades, and fatigue process is viewed as a quasi-static series of discrete crack growth steps. Crack growth process is controlled by the critical value of material stretch and that cyclic loading causes degradation in the critical stretch. When the critical amount of stretch is reached, stable crack growth occurs.

Hygro-thermo-mechanical analysis and failure prediction in electronic packages by using peridynamics

This study presents an integrated approach for the simulation of hygro-thermo-vapor-deformation analysis of electronic packages by using peridynamics. This theory is suitable for such analysis because of its mathematical structure. Its governing equation is an integro-differential equation and it is valid regardless of the existence of material and geometric discontinuities in the structure. It permits the specification of distinct properties of interfaces between dissimilar materials in the direct modeling of thermal and moisture diffusion, and deformation. Therefore, it enables progressive damage analysis in materials or layered material systems such as the electronic packages. It describes the validation procedure by considering a particular package for each thermomechanical, hygromechanical deformation as well as vapor pressure predictions. Also, it presents results concerning failure sites and mechanisms due to hygro-thermo-vapor-deformation.

Peridynamic theory for damage initiation and growth in composite laminate

A recently introduced nonlocal peridynamic theory removes the obstacles present in classical continuum mechanics that limit the prediction of crack initiation and growth in materials. Furthermore, damage growth in composites involves complex and progressive failure modes. Current computational tools are incapable of predicting failure in composite materials mainly due to their mathematical structure. However, the peridynamic theory removes these obstacles by taking into account non-local interactions between material points. This study presents an application of the peridynamic theory for predicting damage progression from a central crack in fiber reinforced composite plates subjected to uniaxial tension loading.

Nonlinear analysis of bonded composite single-lap joints

This study presents a semi-analytical solution method to analyze the geometrically nonlinear response of bonded composite single-lap joints with tapered adherend edges under uniaxial tension. The solution method provides the transverse shear and normal stresses in the adhesive and in-plane stress resultants and bending moments in the adherends. The method utilizes the principle of virtual work in conjunction with von Karmans nonlinear plate theory to model the adherends and the shear lag model to represent the kinematics of the thin adhesive layer between the adherends. Furthermore, the method accounts for the bilinear elastic material behavior of the adhesive while maintaining a linear stress-strain relationship in the adherends. In order to account for the stiffness changes due to thickness variation of the adherends along the tapered edges, their in-plane and bending stiffness matrices are varied as a function of thickness along the tapered region. The combination of these complexities results in a system of nonlinear governing equilibrium equations. This approach represents a computationally efficient alternative to finite element method. Comparisons are made with corresponding results obtained from finite-element analysis. The results confirm the validity of the solution method. The numerical results present the effects of taper angle, adherend overlap length, and the bilinear adhesive material on the stress fields in the adherends, as well as the adhesive, of a single-lap joint.

Nonlinear Analysis of Bonded Composite Tubular Lap Joints

The present study describes a semi-analytical solution method for predicting the geometrically nonlinear response of a bonded composite tubular single-lap joint subjected to general loading conditions. The transverse shear and normal stresses in the adhesive as well as membrane stress resultants and bending moments in the adherends are determined using this method. The method utilizes the principle of virtual work in conjunction with nonlinear thin-shell theory to model the adherends and a cylindrical shear lag model to represent the kinematics of the thin adhesive layer between the adherends. The kinematic boundary conditions are imposed by employing the Lagrange multiplier method. In the solution procedure, the displacement components for the tubular joint are approximated in terms of non-periodic and periodic B-Spline functions in the longitudinal and circumferential directions, respectively. The approach presented herein represents a rapid-solution alternative to the finite element method. The solution method was validated by comparison against a previously considered tubular single-lap joint. The steep variation of both peeling and shearing stresses near the adhesive edges was successfully captured. The applicability of the present method was also demonstrated by considering tubular bonded lap-joints subjected to pure bending and torsion.

Numerical Solution Method

The peridynamic (PD) equation of motion is an integro-differential equation, which is not usually amenable for analytical solutions. Therefore, its solution is constructed by using numerical techniques for spatial and time integrations. The spatial integration can be performed by using the collocation method of a meshless scheme due to its simplicity. Hence, the domain can be divided into a finite number of subdomains, with integration or collocation (material) points associated with specific volumes (Sect. 7.1). Associated with a particular material point, numerical implementation of spatial integration involves the summation of the volumes of material points within its horizon. However, the volume of each material point may not be embedded in the horizon in its entirety, i.e., the material points located near the surface of the horizon may have truncated volumes. As a result, the volume integration over the horizon may be incorrect if the entire volume of each material point is included in the numerical implementation. Therefore, a volume correction factor is necessary to correct for the extra volume. A volume correction procedure required for such a case is described in Sect. 7.2.

Peridynamic Modeling of Granular Fracture in Polycrystalline Materials

A new peridynamic formulation is developed for cubic polycrystalline materials. The new approach can be a good alternative to traditional techniques such as finite element method and boundary element method. The formulation is validated by considering a polycrystal subjected to tension loading condition and comparing the displacement field obtained from both peridynamics and finite element method. Both static and dynamic loading conditions for initially damaged and undamaged structures are considered and the results of plane stress and plane strain configurations are compared. Finally, the effect of grain boundary strength, grain size, fracture toughness and grain orientation on time-to-failure, crack speed, fracture behaviour and fracture morphology are investig ated and the expected transgranular and intergranular failure modes are successfully captured. To the best of the authors’ knowledge, this is the first time that a peridynamic material model for cubic crystals is given in detail.

Impact damage assessment by using peridynamic theory

This study presents an application of peridynamic theory for predicting residual strength of impact damaged building components by considering a reinforced panel subjected to multiple load paths. The validity of the approach is established first by simulating a controlled experiment resulting in mixed-mode fracture of concrete. The agreement between the PD prediction and the experimentally observed behavior is remarkable especially considering the simple material model used for the concrete. Subsequently, the PD simulation concerns damage assessment and residual strength of a reinforced panel under compression after impact due to a rigid penetrator.

Modeling of the onset, propagation and interaction of multiple cracks generated from corrosion pits by using peridynamics

High stress regions around corrosion pits can lead to crack nucleation and propagation. In fact, in many engineering applications, corrosion pits act as precursor to cracking, but prediction of structural damage has been hindered by lack of understanding of the process by which a crack develops from a pit and limitations in visualisation and measurement techniques. An experimental approach able to accurately quantify the stress and strain field around corrosion pits is still lacking. In this regard, numerical modeling can be helpful. Several numerical models, usually based on FEM, are available for predicting the evolution of long cracks. However, the methodology for dealing with the nucleation of damage is less well developed, and, often, numerical instabilities arise during the simulation of crack propagation. Moreover, the popular assumption that the crack has the same depth as the pit at the point of transition and by implication initiates at the pit base, has no intrinsic foundation. A numerical approach is required to model nucleation and propagation of cracks without being affected by any numerical instability, and without assuming crack initiation from the base of the pit. This is achieved in the present study, where PD theory is used in order to overcome the major shortcomings of the currently available numerical approaches. Pit-to-crack transition phenomenon is modeled, and non-conventional and more effective numerical frameworks that can be helpful in failure analysis and in the design of new fracture-resistant and corrosion-resistant materials are presented.