•The non-local volumetric method was used to analyse surface-defected specimens.•Fatigue behaviour of surface-defected specimens under bending and torsion is studied.•Finite element analysis was ...performed to determine the critical volume.•The non-local volumetric method can help engineers in advanced fatigue design.
The influence of defect features on fatigue behaviour is a complex trivial issue. Although the important advances over the last decades, the dialectical relationship between the defect orientation and durability is not clearly understood. The paper aims at studying the influence of the orientation of elliptical defects on the durability of samples made of C45 steel. Three types of samples with elliptical defects were subjected to cyclic bending and torsion (R = -1) in the form of a one-sided notch oriented at various angles, namely 45, 60 and 90°. The stress analysis was performed using local and non-local methods in order to determine an equivalent stress amplitude. The stress fields surrounding the defects were evaluated via three-dimensional numerical models. Then, the results were compared with the results obtained for smooth samples. The results show that the defect orientation has a higher effect under bending loading than under torsion and that the defects oriented perpendicularly to the longitudinal axis of the specimen are more detrimental.
Partition of unity methods (PUM) are of domain decomposition type and provide the opportunity for multiscale and multiphysics numerical modeling. Here, we apply Peridynamic (PD) enrichment to ...propagate cracks in the PUM global–local enrichment scheme. We apply linear elasticity globally and PD over local zones where fractures occur. The elastic fields provide appropriate boundary data for local PD simulations on a subdomain containing the crack tip to grow the crack. Once the updated crack path is found the elastic field in the body and surrounding the crack is updated using the PUM basis with an elastic field enrichment near the crack. The subdomain for the PD simulation is chosen to include the current crack tip as well as features that influence crack growth. This paper is part II of this series and validates the combined PD/PUM simulator against the experimental results. The results of numerical simulation show that we attain good agreement between experiment and simulation with a local PD subdomain that is moving with the crack tip and adaptively chosen size.
•A novel Multiscale Fracture Model using Peridynamic Enrichment of Finite Elements with an Adaptive Partition of Unity•Validation against three experimental data sets.•In addition to the experiments, we validate our hierarchical coupling technique approach with a concurrent coupling approach proposed by Ni et al. using the same experimental data.
In this work, phase-field modeling of hydraulic fractures in porous media is extended towards a Global–Local approach. Therein, the failure behavior is solely analyzed in a (small) local domain. In ...the surrounding medium, a simplified and linearized system of equations is solved. Both domains are coupled with Robin-type interface conditions. The fractures inside the local domain are allowed to propagate and consequently, both subdomains change within time. Here, a predictor–corrector strategy is adopted, in which the local domain is dynamically adjusted to the current fracture pattern. The resulting framework is algorithmically described in detail and substantiated with some numerical tests.
Pre-processing of near-infrared (NIR) spectral data has become a necessary part of chemometrics modeling and is widely used in many practical applications. The objective of the pre-processing is to ...remove physical phenomena in the spectra in order to improve subsequent qualitative or quantitative analysis. Herein, a localized version of standard normal variate (SNV) is proposed, in which the correction parameters are estimated from local spectral areas. The method of determining the optimal spectral segmentation is also presented. Compared with full range methods, the local method demonstrates advantages in spectral linearity correction, model interpretation and prediction accuracy. Several benchmark NIR data sets were studied in our experiments; the proposed method achieved comparable performance against proven full range methods, with the reduction of prediction errors being statistically significant in many cases.
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•A local pre-processing algorithm is proposed for near-infrared spectra.•The optimal segmentation of local areas can be automatically determined by a cross validation scheme.•Experiments show that the proposed local method outperformed the full range pre-processing methods.•The proposed method has no manual parameter and can be easily used in many applications.
According to various experimental results, stiffened panels under compressive loading are prone to debonding between the skin and the flange of the stringer. In this paper, a novel two-way ...global-local coupling approach is presented that is able to model progressive separation of the skin and stringer in stiffened CFRP panels under compression. The main goal of this methodology is to examine skin-stringer debonding at two levels of accuracy, taking advantage of the fast calculations at the global level and assessing in detail the damage propagation at the local level. First, critical areas are defined in a global model with a standard mesh, and local models with a considerably finer mesh are created by means of a submodeling technique. Secondly, a local model analysis is conducted, in which cohesive elements are applied to simulate debonding. Particularly important is the appropriate information exchange in both directions between the different steps of the coupling analysis. Averaged degraded properties are defined at the local model level and transferred back to the global level. The applied compressive load is increased and induces a progression in skin-stringer separation. The global-local coupling loops are repeated until panel failure occurs. The approach is applied to a case of a representative one-stringer stiffened panel and to a stiffened panel for which test results are available. A good correspondence with reference results and test results demonstrates the effectiveness of the global-local approach presented.
This paper outlines a rigorous variational-based multilevel Global–Local formulation for ductile fracture. Here, a phase-field formulation is used to resolve failure mechanisms by regularizing the ...sharp crack topology on the local state. The coupling of plasticity to the crack phase-field is realized by a constitutive work density function, which is characterized through a degraded stored elastic energy and the accumulated dissipated energy due to plasticity and damage. Two different Global–Local approaches based on the idea of multiplicative Schwarz’ alternating method are proposed: (i) A global constitutive model with an elastic–plastic behavior is first proposed, while it is enhanced with a single local domain, which, in turn, describes an elastic–plastic fracturing response. (ii) The main objective of the second approach is to introduce an adoption of the Global–Local model toward the multilevel local setting. In (ii), an elastic–plastic global constitutive model is augmented with two distinct local domains; in which, the first local domain behaves as an elastic–plastic material and the second local domain is modeled due to the fractured state. To further reduce the computational cost, predictor–corrector adaptivity within the Global–Local concept is introduced. An adaptive scheme is devised through the evolution of the effective global plastic flow (for only elastic–plastic adaptivity), and through the evolution of the local crack phase-field state (for only fracture adaptivity). Thus, two local domains are dynamically updated during the computation, resulting in a two-way adaptivity procedure. The overall response of the Global–Local approach in terms of accuracy/robustness and efficiency is verified using single-scale problems. The resulting framework is algorithmically described in detail and substantiated with numerical examples.
•An extension of the Global–Local approach for a ductile phase-field fracture.•A multilevel of the Global–Local formulation through two distinct local domains.•One way adaptivity scheme based on evolution of global plastic flow.•Two-way adaptivity procedure through the information of global hardening flow along with local crack phase-field state.•Compact open-source code for the Global–Local approach: One-dimensional Elasticity.
Wind turbine blades are exposed to numerous impact risks throughout their lifetimes. The impact risks range from bird collisions during operation to impacts with surrounding structures at the time of ...transportation and installation. Impact loads on the fibre composite blades can induce several complex, simultaneously interacting and visually undetectable damage modes and have a high potential to reduce the local and global blade stiffness. An assessment of such impact-induced damages is therefore necessary and usually involves high computational costs using numerical procedures, especially when analysing large composite components. To minimise this computational expense, different numerical impact modelling techniques are utilised, primarily shell-element-based approaches and multiscale-modelling-based global-local approaches. In this article, a comparison between (1) pure shell, (2) shell-to-solid coupling, and (3) submodelling finite element modelling techniques using Abaqus/Explicit is presented for a case where an impactor hits the leading edge of a blade. A high-fidelity local solid finite element model is developed for the leading edge of a DTU 10 MW blade at the region of impact and its stiffness is compared with baseline. A user material subroutine VUMAT for the intralaminar damage mode based on the Hashin failure criterion is formulated and then validated via an experiment from the literature. Finally, based on different numerical modelling techniques, impact investigations are performed, and the impact responses, damage to the blade and computational analysis durations are compared. It is found that the submodelling-based global-local approach is the most efficient analysis technique for this case, capturing failure modes including delamination, core crushing and local surface indentation in the blade. The findings of this study can be used to develop accurate and computationally efficient tools for modelling impact-induced damage to a blade.
•A continuum damage mechanics (CDM) and XFEM based methodology is developed for high cycle fatigue crack growth simulations.•A new damage model is proposed for the evaluation of fatigue crack growth ...life.•A new criterion is proposed based on the damage evolution to identify the appropriate definition of stress triaxiality.•A non-local CDM approach is implemented to reduce the mesh sensitivity.•The present methodology is found quite successful for fatigue crack growth simulations.
In this paper, we have developed a continuum damage mechanics (CDM) based methodology for high cycle fatigue crack growth simulations. A fatigue damage law is proposed and implemented in the framework of extended finite element method (XFEM). A new criterion is proposed based on damage evolution to identify the appropriate definition of stress triaxiality for acquiring the constraint effect on the stress state correctly. Few mesh regularization schemes are also employed for reducing the mesh sensitivity in the results. Simulations are performed on fracture specimens of different materials subjected to constant amplitude fatigue loading. The fatigue life of a turbine disc is also predicted under constant amplitude loading. The results obtained from present methodology (CDM and XFEM) are found in good agreement with the published experimental results. These simulations highlight that the continuum damage mechanics is a simple and effective tool to perform crack growth simulations under high cycle fatigue conditions.
Partition of unity methods are of domain decomposition type and provide the opportunity for multiscale and multiphysics numerical modeling. Different physical models can exist within a partition of ...unity method scheme for handling problems with zones of linear elasticity and zones where fractures occur. Here, the peridynamic model is used in regions of fracture and smooth partition of unity methods is used in the surrounding linear elastic media. Our method is novel in that we evolve the crack path using peridynamics and apply the partition of unity method to compute the elastic fields in the neighborhood of the crack tip. Earlier work uses the peridynamic fields, e.g displacement, at the crack tip to approximate enrichment functions for the partition of unity methods. The method is a so-called global–local enrichment strategy. The elastic fields of the undamaged media provide appropriate boundary data for the localized peridynamic simulations. The geometry of the crack path in the damaged media is transferred to partition of unity method. Here, Heaviside and Westergaard functions are used to model the crack. We do not transfer information of the peridynamic fields to the partition of unity method, solely the crack geometry. The first steps for a combined peridynamic and partition of unity method simulator are presented. We show that the local peridynamic approximation can be utilized to enrich the global partition of unity method approximation to capture the true material response with high accuracy efficiently. Test problems are provided demonstrating the validity and potential of this numerical approach.
•Novel global–local scheme using peridynamics within a partition of unity method•Reduce peridynamic cost while maintaining peridynamic resolution in global response.•Natural peridynamic crack growth in computationally cheap continuum mechanics model.•Foundation for an automatic, combined PD/PUM simulator.
•A new simpler creep-fatigue interaction damage model is developed to predict the life creep fatigue crack growth life of specimen under different hold time conditions.•A new approach based on ...continuum damage mechanics and extended finite element method is developed to perform the creep-fatigue crack growth behavior.•Mixed mode CFCG simulations are performed to show the proficiency of developed coupled approach for solving complex problems.
In this paper, a coupled continuum damage mechanics (CDM) and extended finite element method (XFEM) based methodology is developed to predict the crack growth life under creep-fatigue environment. To predict the life accurately, a new simple nonlinear creep-fatigue interaction (CFI) damage model is presented. In the combined methodology of CDM and XFEM, the XFEM computes stresses in cracked domain and the coined CFI damage equation determines specimen life under creep-fatigue environment. The simulations are performed for different hold time and compared with experiments. The simulated results confirm that proposed CFI damage model along with developed CDM-XFEM framework is a simple and effective methodology for determining creep-fatigue crack growth life efficiently.
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