Virtual Crack Closure Technique Research Articles

Developments in remeshing‐free fatigue crack growth simulation including a new adaptive virtual crack closure technique

AbstractThe present study aims to evaluate and improve the remeshing‐free fatigue crack growth (FCG) simulation and life estimation through two developing FEM‐VCCT and XFEMPN‐VCCT algorithms in Abaqus. First, new energy‐based forms of the Paris, Walker, and Elber FCG models are implemented by a user subroutine, a novel systematic meshing strategy is proposed, and some challenging features of these algorithms are investigated. Despite the success of this methodology in enhancing efficiency, decreasing the run‐time, and preventing potential errors, it is observed that the XFEMPN‐VCCT algorithm has some fundamental errors such as a serious overestimation in FCG life prediction. Thus, a novel “adaptive VCCT” is introduced and implemented by a Python script in Abaqus in the form of a new XFEMPN‐AVCCT algorithm. It is finally concluded that the adaptive VCCT can significantly enhance the accuracy of FCG simulation and life estimation.

Translaminar mode-I fracture toughness experiment of pultruded GFRP laminates using extended compact tension specimen

This paper conducted experiments and theoretic analysis of the fracture performance of pultruded GFRP (Glass Fiber Reinforced Polymers) laminates. The mode-I fracture toughness of pultruded GFRP laminates was evaluated by the eccentrically loaded, Extended Compact Tension (ECT) specimen. The geometry of specimen and experimental procedure refer to ASTM E1922. A total of 16 specimens were tested, which included 0° and 90° roving orientation. Finite element analysis with the Virtual Crack Closure Technique (VCCT) was implemented to calibrate the experimental results. A correction function for normalized notch length was proposed for pultruded GFRP translaminar fracture toughness. Carpet plot was designed to discuss the relationship between fiber volume ratio and fracture toughness, which demonstrated that the fracture toughness strongly correlated with the fiber volume ratio. Also, the effect of fraction of 0° layers on fracture toughness and material orthotropy was studied. The relationship of material orthotropy parameter and fracture toughness was discussed.

Novel bi-layer beam elements for elastic fracture analysis of delaminated composite beams

A general finite element method is proposed for linear elastic fracture analysis of delaminated bilayer composite beams. An interface deformable bilayer beam model is adopted in modeling the virgin portions of bilayer beams, and it is capable of guaranteeing the continuity condition of internal forces at the tip of delamination because the bilayers are modeled as two separate shear deformable sub-beams and both the interface normal and shear compliances are introduced to account for interface deformation. The stiffness matrices of bilayer beams using the linear and quadratic interpolation polynomials are both derived using the principle of minimum potential energy. Then, a finite element program is developed by assembling the element stiffness matrices of virgin and delaminated portions of bilayer beams and applying the corresponding equivalent nodal forces. Two typical fracture specimens (i.e., single leg bending and end-notched flexure bilayer beams) are analyzed using the proposed bilayer beam elements. The computed displacement and energy release rate are compared well with those of analytical solutions, and the mode components of energy release rate for single leg bending specimen are also obtained using the virtual crack closure technique. It demonstrates that the proposed novel bilayer beam elements are capable of effectively and efficiently predicting the displacement and energy release rate (including its mode components) of delaminated bilayer beams. The developed bilayer beam element is general in nature and accurate and efficient in particular, because it can achieve the same accuracy as the high order beam theory and be easily implemented in the existing commercial finite element software.

Numerical frequency and SERR response of damaged (crack/delamination) multilayered composite under themomechanical loading: An experimental verification

This research predicted the influences of combined damage (delamination and crack) and thermomechanical loading on the modal values and strain energy release rate (SERR) of the curved shell panel. The results are obtained computationally using a computer code (MATLAB platform) with the help of isoparametric finite element (FE) steps and the higher-order deformation polynomial. The Hamilton principle is adopted to obtain the final governing equation for the frequency analysis of the damaged structure. Additionally, the deflection, strain, and stresses are recorded by back substituting the numerical solutions to compute the desired energy values. The obtained solution accuracy and the stabilities are verified by performing the convergence and the comparison (published frequencies and SERR) studies. Moreover, a few lab-scale modal experimentations (cracked laminated composite with and without temperature increments) are carried out to accomplish the proposed model. Lastly, a series of numerical examples related to the SERR and modal responses of the current damaged curved composite structure is solved by considering the geometrical, material, and damage parameters (shape and sizes of delamination and orientation of crack). The SERR values calculated using the virtual crack closure technique. The pointwise comprehensions related to the inputs and the model are envisaged in details.

An explicit delamination propagation algorithm to simulate delamination growth under quasi-static and fatigue loading without re-meshing using virtual crack closure technique and progressive nodal release

A modeling approach is proposed to simulate delamination propagation in composite laminates under both quasi-static and fatigue loading regimes. Delamination growth is simulated using the Virtual Crack Closure Technique combined with a progressive nodal release strategy. In the proposed approach, the delamination propagation increment is determined explicitly, based on the energy release rate calculated in the previous time increment. Explicitly determining the delamination propagation increment linearizes the system of equations that results from the progressive nodal release strategy and eliminates convergence issues associated with delamination growth. In fatigue, the delamination growth increment is calculated using as input growth rates characterized experimentally via fitting of a suitable form of the Paris law to the experimental data. Under quasi-static loading conditions, a sufficiently large pseudo-growth rate is assumed, such that the simulation results converge to the results obtained with the chosen binary (growth/no growth) fracture criterion. Since both fatigue and quasi-static loading regimes share the same underlying algorithm, simulating the transition between fatigue and quasi-static delamination growth is trivial. The approach is demonstrated to accurately simulate delamination growth for all cases assessed, including quasi-static mixed-mode loading and the transition between fatigue and quasi-static delamination growth regimes. Finally, it is also shown that the approach can simulate both self-similar and non-self-similar delamination growth.

Multi-Crack Dynamic Interaction Effect on Oil and Gas Pipeline Weld Joints Based on VCCT

In pipelines for transporting oil and gas, multiple cracks often exist in weld joints. The interaction among the cracks should be considered as it directly affects the life span of the pipeline structures. In the current investigation, based on the fluid–solid magnetic coupling model, the virtual crack-closure technique (VCCT) is applied to systematically study the multi-crack dynamic interaction effect on pipeline welds during the crack propagation process. The results show that the existence of an auxiliary crack accelerates the main crack’s propagation. When the auxiliary crack is nearer to the main crack tip, the enhancement effect of the auxiliary crack on the main crack increases. Further, when the initial length of the auxiliary crack increases, the main crack becomes easier to propagate. Two important parameters, the distance between the two interacting crack tips and the initial size of the auxiliary crack, are studied in detail. Their interference effect on the main crack has been quantified, which is very user-friendly for engineers to conduct failure assessment and prevention for oil and gas pipes with multiple cracks at weld joints.

Fracture toughness resistance curves for a delamination in CFRP MD laminate composites, Part I: Nearly mode II deformation

In this investigation nearly mode II initiation and resistance energy release rate values, required for delamination propagation, were determined based on quasi-static calibrated end loaded split (C-ELS) fracture tests. Two multi-directional (MD) carbon fiber reinforced polymer (CFRP) material systems were examined. The first was manufactured as a wet-layup, with an initial delamination between a unidirectional ply and a plain woven ply. The second was manufactured from a prepreg, with an initial delamination along an interface between two plain woven plies oriented differently. Two-dimensional finite element analyses (FEAs) of the tested specimens were performed. Based upon the FEA results, with use of the displacement extrapolation (DE) method, as well as the virtual crack closure technique (VCCT), stress intensity factors were calculated. The obtained values were used to determine the in-plane mixed-mode phase angle for each test, which indicated nearly mode II deformation. Fracture toughness resistance curves or R-curves were generated as a function of the delamination extension. The critical initiation and resistance energy release rate values were obtained from the stress intensity factors, as well as with the J-integral, which are local methods. In addition, the global experimental compliance method (ECM) was used. Small differences were observed between the results obtained by means of the two methods. From a comparison between the R-curves of the two material systems, it was seen that the initiation energy release rate values were higher for the prepreg by 25.5%. A greater difference was found in the increasing portion of the R-curves, as well as the steady state energy release rate values.

Characterization of the interlaminar fracture toughness of unidirectional thermoplastic composites

In this study, the critical energy release rate in mode I (G1c) for thermoplastic composites made of carbon fiber (CF) and glass fiber (GF) with a polyamide 6 (PA6) matrix is investigated. Double cantilever beam (DCB) was used as the specimen for the mode I test, and the ASTM D 5528-13 was chosen as standard. Moreover, different methodological approaches were applied by comparing different data reduction schemes from the ASTM D 5528-13 and further analytic approaches from the literature. In addition to the conducted experiments, a numerical model of the DCB test is developed and the virtual crack closure technique (VCCT) is performed on the numerical model to determine G1c for PA6-CF and PA6-GF. For the interlaminar fracture toughness G1c a value of 2.87 mJ/mm2 was determined for PA6-GF and a value of 2.16 mJ/mm2 for PA6-CF, which indicate that the use of PA6 as matrix in a composite structure leads to good resistance to damage. A comparison of the different methodological approaches showed a good agreement between the analytical approaches from the literature and the ASTM D 5528-13. In contrast, the values generated for G1c by the VCCT method were significantly higher than those of the other methods.

Copper to resin adhesion characterization for power electronics application: Fracture toughness and cohesive zone analysis

The use of molding compound as encapsulant is nowadays increasing in semiconductor power module applications. The adhesion of package interfaces between copper components and molding compound is one of the key aspect for an improved durability. The presented activity proposes the fracture toughness characterization of copper–resin interface in a power semiconductor package due to different experimental tests and the cohesive zone method to describe interfacial fracture. Double Cantilever Beam (DCB) and Four Point Bending (FPB) tests have been executed on dedicated bi-material coupons. The scope of these trials has been to enhance two different propagation modes based on different ratio between mode-I (opening) and mode-II (sliding) according to a mixed-mode approach. Strain energy release rate (SERR) and mode-mixity have been estimated by a finite element analysis based on the virtual crack closure technique (VCCT) and the crack surface displacement method (CSD). The information about fracture toughness at two different mode mixity have been considered to predict the SERR for every arbitrary mode mixity. Finally, dedicated finite element models based on cohesive elements have been developed and calibrated considering the fracture toughness experimental values and the measured force–displacements behavior during the two considered tests. Dedicated physical analyses have been carried out to validate the proposed method.

Extension of the virtual crack closure technique to cracked homogeneous bodies undergoing large deformations

In this work, energy release rates evaluated by means of the virtual crack closure technique (VCCT) are analyzed for structures undergoing large deformations. For this, nonlinear finite element (FE) analyses are carried out on edge notched and pure shear specimens in Abaqus. Two hyperelastic constitutive material models: incompressible Mooney–Rivlin (I-MR) and incompressible Ogden (I-Ogden) were used. For the nonlinear elastic analyses, the relationship between the force and displacement at a node may not be linear. Hence, the nodal point forces need to be integrated over the corresponding displacements to evaluate the energy release rates. The need for transforming the nodal point forces and displacements into a local nodal coordinate system to determine the energy release rates and mode mixity is examined. The relation between the total energy release rates GT evaluated from the nodal point forces and displacements in the global and local nodal coordinate system is derived analytically and analyzed numerically. Finally, GT evaluated by VCCT for the pure shear and edge notched specimens are compared to the J-integral.

Numerical Evaluation of Fatigue Crack Growth of Structural Steels Using Energy Release Rate with VCCT

This research presents the numerical evaluation of fatigue crack growth of structural steels S355 and S960 based on Paris’ law parameters (C and m) that are experimentally determined with a single edge notched tension (SENT) specimen using optical and crack gauge measurements on an electromotive resonance machine at constant amplitude load. The sustainable technique is replacing destructive, time-consuming and expensive approaches in structural integrity. The crack propagation is modelled using the 3D finite element method (FEM) with adaptive remeshing of tetrahedral elements along with the crack initiator elements provided in simulation software for crack propagation based on linear elastic fracture mechanics (LEFM). The stress intensity is computed based on the evaluation of energy release rates according to Irwin’s crack closure integral with applied cyclic load of 62.5 MPa, 100 MPa and 150 MPa and stress ratios of R = 0 and 0.1. In order to achieve optimized mesh size towards load cycle and computational time, mesh and re-mesh sensitivity analysis is conducted. The results indicate that the virtual crack closure technique VCCT-based 3D FEM shows acceptable agreement compared to the experimental investigation with the percentage error up to 7.9% for S355 and 12.8% for S960 structural steel.

Thermomechanical Analysis of a Reactor Pressure Vessel under Pressurized Thermal Shock Caused by Inadvertent Actuation of the Safety Injection System

The damage induced pressurized thermal shock (PTS) may pose to a reactor pressure vessel (RPV) is a critical safety requirement assessed as part of the ageing management programme of pressurized water reactors (PWRs). A number of researches have studied PTS initiated mainly by postulated accidents such as loss of coolant accidents (LOCAs). However, investigations on PTS-induced threat on RPV caused by inadvertent actuation of the safety injection, a frequent anticipated transient, have not been thoroughly studied. In this paper, a simplified multistep analysis method is applied to study the thermomechanical status of a two-loop PWR under PTS loads caused by inadvertent actuation of the safety injection system. A direct-coupling thermomechanical analysis is performed using a three-dimensional (3D) RPV finite element model. A 3D finite element submodel (consisting of the highiest stress concentration area in the RPV) and an assumed crack are then used to perform fracture mechanics analysis. Subsequently, the critical integrity parameter-stress intensity factor (SIF) is estimated based on FRANC3D-M-integral method coupled in the multistep simulation. The material fracture toughness of the vessel is computed based on the master curve method with experimental fracture toughness data. The results obtained from the direct coupling stress analysis in comparison with sequential coupling approach demonstrate the effectiveness of the proposed multistep method. Also, comparing SIF results obtained with that calculated based on the conventional virtual crack-closure technique (VCCT) and extended finite element method (XFEM) show good agreement. This study provides a useful basis for future studies on anticipated transient-induced crack propagation and remaining service life prediction of ageing reactor pressure vessels.

Experimental and computational assessment of disbond growth and fatigue life of bonded joints and patch repairs for primary airframe structures

The applicability of a damage slow growth management strategy to bonded joints/patch repairs of primary aircraft structures was evaluated through an experimental and computational study. Fatigue tests were conducted to investigate the entire process of disbond growth from initiation up to joint ultimate failure. The residual static strength of the joint as a function of disbond length was established using finite element modelling, in which the mesh size was calibrated using the static strength of the specimens measured in room temperature and dry (RD) and hot-wet (HW) conditions, based on the characteristic distance approach. A virtual crack close technique (VCCT) approach was utilised to assess the strain energy release rates (SERRs) as a function of disbond crack length. The measured disbond growth rates were correlated with the SERRs using a modified Paris law that enabled prediction of joint fatigue life. The fatigue test results indicated that for a joint having a sufficient static strength safety margin under a typical fatigue loading that would propagate disbond, the disbond growth would be stable in a particular length range. Thus, the slow growth approach would be feasible for a bonded joint/patch repairs if the patch is designed to be sufficiently large to allow extended damage propagation (whilst in the case when patch size must be limited, safe-life design for the patch termination region in critical repairs must be considered. Should disbond growth occur in this case, the joint must be repaired or replaced). The work presented in this paper validated the framework/procedure proposed previously by the authors (Tanulia et al., 2020) for managing damage slow growth in bonded joints/patch repairs. In the last part of this paper the planned follow-on research is briefly described.

Numerical prediction of static and vibration responses of damaged (crack and delamination) laminated shell structure: An experimental verification

This research reported the influences of combined damage (delamination and crack) on the layered structure numerically via finite element technique in a higher-order mathematical model framework. In this regard, the modal responses and the strain energy release rate (SERR) are calculated by considering the influences of the delamination and/or crack within the flat/curved laminated structure. Moreover, the virtual crack closure technique (VCCT) has been adopted to compute the structural responses of the layer cracked composite structure, i.e., the SERR values. Further, the exactness of the present model is proven by comparing the frequency and SERR values with the previously published data from the open domain. Additionally, the model validity is certified through the different comparisons with in-house recorded experimental eigenvalues. The composite shell structures are examined for eigenvalue and SERR to assess the effects of delamination and/or crack by altering the input variables to show the applicability of the present model.

Thermo-electro-mechanical dynamic fracture analysis on laminated piezoelectric plates

A thermo-electro-mechanical extended layerwise method (TEM-XLWM) is established for the multi-physical dynamic problems of piezoelectric laminates with delaminations or/and transverse cracks. The proposed method is deduced from the thermo-electro-mechanical mixed variational principle. The strong discontinuous functions and classical the extended finite element method (XFEM) are used to model delaminations and the transverse cracks, respectively. The Newmark integration algorithm and Crank–Nicolson scheme are combined to solve the transient multi-physical fields simultaneously. In the numerical example analysis, the proposed dynamic fracture analysis method is verified by a three-dimensional model. The laminated piezoelectric plates with delamination and/or transverse cracks are analyzed and the strain energy release rate (SERR) is calculated based on the virtual crack closure technique (VCCT).

Simulation of crack growth in residual stress fields of pre-fatigued T-welded joints repaired by tungsten inert gas: a 3D approach

In this article, a three-dimensional finite element model (FEM) is used to predict the crack growth at the weld toe of a pre-fatigued T-joint that was repaired with a remelting technique. The numerical models were developed using the MSC.Marc software. Fatigue life is estimated by integrating the Paris-Erdogan law. The stress intensity factors are obtained by the virtual crack closure technique (VCCT).The T-welded joints, made of S355 steel, are obtained by covered electrode process and pre-cracked by fatigue. These welded joints were repaired by TIG dressing. The stress field generated by this dressing technique was estimated using a FEM model, presented in authors’ previous works. For the crack growth was used the VCCT three-dimensional model recently presented by the authors to predict the effect of overloads. The pre-existence of an elliptical crack at the weld toe, with a depth of 0.5 mm was considered. It is also studied the growth of pre-existing cracks which have been poorly repaired.It was observed that the TIG dressing produce residual compression stress fields on the weld toe that causes a delay in crack growth. The obtained results are compared with experimental ones. The fatigue’s lives obtained by simulations with the numerical model presented in this paper allows to evaluate the application conditions of TIG remelting technique in the repair of pre-cracked welded joints.

Numerical Fracture Analysis of a Reactor Pressure Vessel based on Abaqus-FRANC3D Co-simulation Method

The reactor pressure vessel (RPV) is subjected to many cyclic loadings critical of which is the integrity risk posed by pressurized thermal shock (PTS) loadings induced by one of the most frequent anticipated operational occurrences - inadvertent operation of the safety injection system (SIS). In this paper, the fracture mechanics analysis for an ageing pressurized water reactor subjected to PTS induced by inadvertent actuation of the SIS is performed using a proposed simplified Abaqus-FRANC3D co-simulation method. A three-dimensional (3-D) finite element half-symmetric model of a typical pressured water reactor RPV is used to perform thermal-mechanical stress coupling analysis. 3-D fracture mechanic submodel with an assumed surface crack is created for the computation of the transient integrity parameter-stress intensity factor (SIF), using M-integral approach coupled in the proposed co-simulation method. Subsequently ASME method is used to evaluate the vessel’s material fracture toughness. Finally, the SIFs obtained with the simplified co-simulation method is compared with the conventional virtual crack-closure technique (VCCT), and the result show good agreement. This work serves as a useful reference for fast crack propagation and life prediction analysis of ageing PWR RPVs.

Effect of bimodularity and thermomechanical stresses from composite curing on mixed-mode fracture behavior of functionally graded skin-stiffener runout

ABSTRACT The present work illustrates the influence of bimodulus polarity and curing stress on interface delamination in skin stiffener runout. In contrast to unimodular assumptions, the bimodulus skin stiffener’s fracture behavior is much more unsymmetrical depending on the sequential thermo-mechanical loading. The numerical study has been done to demonstrate debonding and delamination with the help of the Virtual Crack Closure Technique on compliant runout configuration under varying bimodular ratios. The modified design of the runout has been displayed, and different design configurations have been compared to determine the merits of the design of skin-stiffener runout: a baseline configuration, a tip-tapered configuration, and notch-tapered configuration with the functionally graded bimodular property. A three-dimensional finite element-based analysis has been performed on these configurations to evaluate the strength and damage tolerance. Also, the Strain Energy Release Rate has been assessed for non-identical loading and boundary conditions. It has been found that bimodularity significantly reduces failure growth. This analysis aims to decelerate the interfacial fracture extension rate by introducing functionally graded bimodularity in the structure.

Nonlinear ABAQUS Simulations for Notched Concrete Beams.

The numerical simulation of concrete fracture is difficult because of the brittle, inelastic-nonlinear nature of concrete. In this study, notched plain and reinforced concrete beams were investigated numerically to study their flexural response using different crack simulation techniques in ABAQUS. The flexural response was expressed by hardening and softening regime, flexural capacity, failure ductility, damage initiation and propagation, fracture energy, crack path, and crack mouth opening displacement. The employed techniques were the contour integral technique (CIT), the extended finite element method (XFEM), and the virtual crack closure technique (VCCT). A parametric study regarding the initial notch-to-depth ratio (ao/D), the shear span-to-depth ratio (S.S/D), and external post-tensioning (EPT) were investigated. It was found that both XFEM and VCCT produced better results, but XFEM had better flexural simulation. Contrarily, the CIT models failed to express the softening behavior and to capture the crack path. Furthermore, the flexural capacity was increased after reducing the (ao/D) and after decreasing the S.S/D. Additionally, using EPT increased the flexural capacity, showed the ductile flexural response, and reduced the flexural softening. Moreover, using reinforcement led to more ductile behavior, controlled damage propagation, and a dramatic increase in the flexural capacity. Furthermore, CIT showed reliable results for reinforced concrete beams, unlike plain concrete beams.

Analysis of mode II strain energy release rates in end-notched flexure tests of carbon fiber-reinforced plastic curved beams

The present study aims to formulate strain energy release rates (SERR) for curved beams, which are supposed to be cut from tanks or cylinders, in End-Notched Flexure (ENF) tests based on Euler-Bernoulli’s and Timoshenko’s curved beam theories. The derived SERRs based on the curved beam theories were compared with those based on the flat beam theory for specimens with various geometries to prove the validity of using the curved beam theory in the ENF tests of curved beams. The validity of the derived compliance and SERRs was verified for the specimens with various geometries using a two-dimensional finite element analysis, in which virtual crack closure techniques were used to calculate the SERRs. The results revealed that Euler–Bernoulli’s curved beam theory was effective in cases with large radius-of-curvature-to-thickness (R/h) values but not in those with small R/h values, whereas Timoshenko’s curved beam theory was effective even for small R/h values.