Crack Front Shape Research Articles

Effect of fiber orientation of adjacent plies on the mode I delamination fracture of carbon fiber reinforced polymer multidirectional laminates

AbstractThe extensive use of multidirectional composite laminates requires to understand the delamination behavior at interfaces between plies with different fiber orientations. In this study, double cantilever beam testing was performed to investigate the mode I interlaminar fracture of carbon fiber reinforced polymer laminates with different central interfaces (0//0, 0//+45 and +45//−45). X‐ray microtomography revealed the curved crack front shape that was incorporated to calculate fracture toughness. The fracture toughness varies with the crack length in a typical delamination resistance curve, which can be quantified by an empirical equation. Incorporation of variable fracture toughness into a cohesive zone model can better predict the delamination fracture of the laminate, compared to constant toughness. It was found that the delamination mechanism is independent of central interfaces. However, compared to unidirectional laminates, multidirectional laminates are less resistant to crack initiation, but more resistant to propagation with higher toughness and shorter fiber bridging zone.Highlights Mode I interlaminar fracture of CFRP laminates with different central interfaces was investigated experimentally and numerically. Curved crack front shape was incorporated to calculate fracture toughness. Incorporation of variable fracture toughness into a cohesive zone model can better predict the delamination fracture of the laminate. Multidirectional laminates are less resistant to crack initiation but more resistant to propagation with higher toughness and shorter fiber bridging zone.

Prediction of the Crack Front Shape of the Corner Interface Crack

This study delves into the analysis of interface crack propagation originating from a right-angle corner along the bonding plane between the two plates composed of dissimilar materials. The research explores three distinct crack front shapes: concave, triangular, and convex (quarter-circle). The obtained results, meticulously presented in this paper, offer valuable insights into the nature of the crack propagation along these geometries. The findings elucidate that in the case of a convex crack front, the edges demonstrate a significantly accelerated propagation compared to the rest of the crack front. Conversely, for the triangular and concave crack fronts, the central region experiences faster propagation compared to the edges. These revelations lead to a generalized conclusion regarding the stability of different crack front shapes, highlighting the triangular crack front as the most stable configuration in this context. The implications of these observations provide essential knowledge for understanding and managing crack propagation in composite structures, offering potential applications in various engineering domains.

An efficient model for predicting complex delamination front of elastic coupling laminates

This work proposes a simple and efficient model to predict the variable crack front with any shape. The model contains a propagation criterion which defines the local growth direction of the delamination crack front by the vector perpendicular to the connection line of two adjacent mesh points. The angle between this vector and the pre-crack direction is calculated by the coordinates of two delamination front points. Crack front can be obtained by the local direction changes of the historical crack front. This model avoids the computing time caused by a high-fidelity finite element model. Its applicability is verified for composite laminates without coupling and with different couplings. The predicted crack front shows good agreements with the numerical results obtained by a high-fidelity FE model with refined mesh. Factors controlling the crack front shape are further discussed by analyzing strain energy release rate and mode mixture distribution at the crack front.

Numerical modelling of fatigue crack closure and its implication on crack front curvature using ΔCTODp

One of the widely used approaches to characterize fatigue crack propagation is the use of the effective stress intensity factor range ΔKeff, which relies on determination of crack closure value Kcl. The used models of crack closure are most frequently-two-dimensional, however, for real cracks, the 3D effects should be taken into account. The paper presents 3D finite element analyses of the influences of crack front shape, inserted cycles (loading cycles between node releases) and crack closure on the crack driving force in terms of ΔKeff and ΔCTODp (plastic part of crack tip opening displacement range). Numerically obtained crack closure depended on the simulation strategy. In the case of inserted cycles, crack closure disappeared in the internal part of the specimen and remained only near the free edges. The use of ΔCTODp had the advantage of a well-defined parameter in situations where ΔKeff was problematic, namely at the corner points, which did not allow finding of equalized crack driving force along the whole crack front using ΔKeff. Equalized crack driving force in terms of ΔCTODp was found for crack front curvature with the edge angle 15.4° in simulation with crack closure, which was in good agreement with the experimentally measured value of 16°. Loops produced by loading and unloading branches of the force vs CTOD diagrams helped to describe the crack closure process and magnitude. Actual values of CTOD did not agree with the classical idea of 2D solutions under plane strain and plane stress. CTOD was larger in the internal part of the specimen than at the free edges, even in simulations with no crack face contact.

Dynamic Behavior Analysis of a Rotating Shaft with an Elliptical Breathing Surface Crack

PurposeIn this paper, dynamic behavior of a rotor system with an elliptical breathing crack that simulates the real shape of the crack front is investigated.MethodsA finite element model of the cracked rotor system is developed. The crack breathing mechanism is modelled based on an improved breathing model which considers the inclination of the neutral axis of the cracked element cross-section during shaft rotation. Harmonic balance method is used to solve the equations of motion of the rotor system for steady-state response characteristics. The effect of some parameters such as crack depth, crack shape factor and the spinning speed is investigated.Results and conclusionsThe results show that the unique whirl orbits behavior during passage through the subcritical speeds serve as a key indicator of crack presence in the shaft. The effects of the crack front curvature and the breathing model are revealed. The value of shape factor affects the whirl orbit characteristics such as size of the inner or outer loops and the amount by which the orbits rotate while crossing the subcritical speeds. The presented model considering the real crack front shape may contribute towards improved modelling of cracked rotors and better interpretation of measured vibration response.

Benchmark test for mode I fatigue-driven delamination in GFRP composite laminates: Experimental results and simulation with the inter-laminar damage model implemented in SAMCEF

Adopting effective and accurate numerical tools capable of predicting damage effects on the structure reduces design, certification, and maintenance costs. However, the tools to assess progressive delamination under high-cycle fatigue are rarely validated against realistic benchmark tests different from simple tests on coupon specimens that can be simplified to a 2D geometry. This work presents a benchmark test on a demonstrator specimen made of a non-crimp fabric laminated Glass Fiber Reinforced Polymer (GFRP) used in the wind energy industry. The case shows varying crack growth rates and crack front shape over the fatigue life, making it more representative of structures in service than coupon specimens. Moreover, the test is simulated with the first commercially available tool to assess progressive delamination under high-cycle fatigue loading based on a cohesive zone model approach. The method is implemented in the Simcenter Samcef 2021.2 software package dedicated to mechanical virtual prototyping. A characterization testing campaign on coupon specimens is carried out to obtain the material properties for the method. The numerical method can reproduce the experimental results on the demonstrator specimen regarding crack front shape evolution and crack front location versus the number of fatigue cycles.

Three‐dimensional fatigue crack growth simulation and fatigue life assessment based on finite element analysis

AbstractDamage tolerance design allows manufactures to assess fatigue crack propagation of components containing initial defects. A new modeling approach is proposed to carry out a systematic crack growth analysis based on an analytical method using reduced order models and three‐dimensional (3D) finite element (FE)‐based fatigue crack growth (FCG) analysis. 3D FE‐based FCG analysis is adopted as an advanced modeling approach for component geometries without any simplifications with respect to crack front shape or planarity of the crack path. The FE‐based FCG approach was verified and validated in two different stages: Ti‐6Al‐4V plate geometry with three different single elliptical crack configurations and Al 2024‐T3 specimens with two different multiple crack configurations. The analytical FCG approach was developed to estimate crack front evolution and crack growth life for three different elliptical cracks to verify the FE‐based approach. Experimental data of Al 2024‐T3 specimens with multi‐edge cracks was used to further validate the FE‐based FCG approach. The FE‐based FCG approach proved to be both accurate and powerful in assessing crack propagation life and crack paths of structural parts.

The crack shape evolution in unstable, flexural fractures for soda-lime glass beams by phase-field analysis

In this work, phase-field simulations were used to investigate the unstable crack propagation in brittle plates fractured in bending. The evolution of crack front shapes was studied considering over 20 scenarios and accounted for both the effects of the Poisson’s ratio and the plate’s width. The crack front in unstable cracks was found to be nearly elliptical only when the cracks were relatively short, with depths less than half the plate’s thickness. In general, unstable cracks resulted in intersection angles of 88°±6° between the crack front and the free surface. Higher Poisson’s ratios led to more oblong cracks but had no obvious effects on the intersection angles. It was found that the evolution of the crack shape was unaffected by the plate’s finite width up to crack lengths equal to 80% of the plate’s width. A cursory literature review on flexural fatigue cracks in steel and on subcritical crack growth in glasses suggested that the description of the crack front proposed in this work could also accurately describe the crack shapes for these types of fractures. However, differences in the behavior among these cases became more evident for crack depths larger than 60% of the plate’s thickness.

Quantitative evaluation of fracture toughness deterioration due to Pre-strain

Previous studies presented the fracture toughness evaluation values decrease due to pre-strain by local compression. However, it was not possible to distinguish whether the cause was fracture toughness deterioration or poor crack front shape straightness due to a bowing crack front at low strain. The authors applied pre-strain without affecting the crack front shape and conducted fracture toughness tests showing that 1% pre-strain reduces fracture toughness by 50%. Furthermore, we investigated the effect of the pre-strain direction on fracture toughness, and proposed a method for converting longitudinal pre-strain to thickness direction strain and demonstrated its effectiveness.

Holistic determination of physical fracture toughness values and numerical parameters for delamination analysis considering multidirectional-interfaces

Delaminations are a concern for the structural integrity of fibre composite structures. The decisive material parameter for delaminations is fracture toughness. Structures usually have a multidirectional ply stacking. However, interface orientation dependant fracture toughness values and R-curve effects are neglected in numerical delamination analysis. This work investigates interface orientation specific fracture toughness values and considers R-curve effects in mode I to improve simulation accuracy. Therefore, mode I, mode II and mixed mode fracture toughness values of different interface ply orientations are determined experimentally and verified using numerical analysis of the characterisation specimens with cohesive zone modelling. In this way, an engineering methodology is provided for the experimental characterisation and comprehensive numerical modelling of delaminations in mesoscale progressive damage analysis of multidirectional composite structures. In addition, a full parameter set for the simulation of four different interfaces of M21-T700GC prepreg material is given. It can be shown that the use of standard 0°//0°-values leads to very conservative results. The use of interface specific values increases the accuracy. Ultrasonic scans of the DCB specimens are used to compare the crack front shapes for validation. Not only the load displacement curves of the characterisation specimens are well captured, but also the crack front shapes. This demonstrates that by smearing the microscale effects, the material behaviour can be captured phenomenologically correct by mesoscale modelling suitable for industrial use.

Assessment of fatigue crack growth based on 3D finite element modeling approach

Fatigue crack growth life assessment enables manufacturers to quantify damage tolerance capability of high-risk components. Reduced order models that are based on simple geometries (i.e. surface crack in a plate, corner crack at a bolt hole) and on the assumption that cracks maintain an elliptical shape during propagation, are commonly employed in the damage assessment. A more comprehensive modeling process should consider the component geometry, service loading conditions and, eliminate assumptions related to crack front shape or planarity of the crack growth path. A 3D finite element-based approach is evaluated in this study as a more accurate alternative to reduced order models. For verification purposes, an analytical solution-based model was developed and implemented in MATLAB to predict fatigue crack growth life and crack front evolution for three different crack types: surface, corner and internal. The analytical model solutions are compared against 3D finite element (FE) based approach implemented in SimModeler Crack. The 3D FE modelling approach has been further tested and validated against experimental fatigue crack growth measurements from two Al 2024-T3 specimens containing multiple cracks. The verification and validation data presented herein show that the 3D FE-based modelling approach provides an accurate and effective modelling tool for crack propagation life assessment of structural components.

A consistent energy-based cohesive zone model to simulate delamination between differently oriented plies

A consistent energy-based cohesive zone model to simulate the mode I delamination behaviour of Fully-Uncoupled Multi-Directional (FUMD) laminates is presented in this study. The proposed energy-based approach allows determining a more general constitutive response of the cohesive interface to better match the experimental results. The constitutive behaviour of the interface is implemented in a standard finite elements (FE) code by means of a user-defined subroutine. To perform the simulations, FE models of a Double Cantilever Beam (DCB) specimen are developed with standard and multidirectional interfaces. The results of the simulations are compared to the experimental ones in terms of force–displacement curves and crack front shape to assess the effectiveness of the proposed model. The comparison shows that the numerical simulations can closely replicate the opening delamination behaviour of DCB specimens during propagation and, in particular, they capture quite well the shape of the delamination fronts with some differences: numerical delamination fronts are characterised by a curvature lower than the one of the experimental counterparts, especially towards the specimen edges. Simulations carried out for different initial delamination lengths confirmed that the delamination changes its front shape at the very beginning of the propagation, then the front remains unaltered. The length of the transition zone for the shape of the delamination front has been found to be much lower than the specimen width.

On the key role of crack surface area on the lifetime of arbitrarily shaped flat cracks

Accurate fatigue lifetime prediction is a central element in many industries. Often, a damage tolerant approach is used to ensure that some given imperfections are safe. In this context, these lifetime predictions are frequently made using simplified crack geometries leading to costly conservatism. In particular for a closed crack front, a circular or elliptical crack enclosing the real defect is generally used leading to an underestimation of the real lifetime. Using an iterative perturbation method to simulate the fatigue growth of many tensile complexly shaped cracks, we show that in the absence of any additional complexity, (i) the front quickly becomes circular; (ii) its evolution with the number of loading cycles can be obtained analytically using a circular crack of same area as the original distorted defect. In practice, it means that replacing a complex crack front shape with this simple, analytically solvable configuration is an effective way to improve predictions and that it is not useful to invoke more complex shapes such as elliptical cracks. These take-home messages are illustrated by an example from the aviation industry.

Assessment of a numerical strategy for fatigue growth and shape evolution of a corner crack from a pin-loaded hole

The study investigates fatigue growth and shape evolution of a corner crack in a pin-loaded hole by means of three-dimensional FE analyses. The constraint factor/plasticity-induced crack closure strategy was tuned to reproduce experimentally measured crack front shapes. The study quantitatively determines the LEFM acceptability regions using elastic–plastic simulations. It also assesses the sensitivity of crack propagation and shape evolution to the stress distribution along the front, to the relationship between J-integral and stress intensity factor, and to changing propagation rates along different directions. The proposed approach produces very accurate results in terms of crack propagation rate and shape evolution.

3D predictions of the local effective stress intensity factor as the fatigue crack propagation driving force

The objective of this study is to develop a numerical tool using the commercial software, Abaqus and Python, to predict the fatigue crack front shape while taking into account the influence of plasticity induced crack closure on crack propagation in three Dimensional (3D) structures. In this aim, a 3D model of a compact tension specimen made out of stainless steel 304L, and subjected to a constant loading scheme, is proposed. The crack propagation is considered to be driven by the stress fields developed in the vicinity of the crack tip and thus by the stress intensity factor K. Two parallel simulations are used: an elastic simulation intends to calculate the local maximum stress intensity factor while the other, an elasto-plastic one, aims at obtaining the plastic wake and the resulting crack closure load. The results of both simulations are combined in order to constitute the effective stress intensity factor range, which is in turn used, along with Paris law, to calculate the crack propagation along the thickness. The local crack advancements obtained allow to construct the new crack front. Finally, a node release technique is used with geometry remeshing to issue new iterations with new boundary conditions that respond to the changes in the crack front. The procedure is repeated until the stabilization of the effective stress intensity factor values all along the specimen thickness is reached. The results obtained are compared with previously issued experimental results, showing very good results in small scale yielding and beyond that a large dependency on the plastic zone size developed in the neighborhood of the crack front.

Advantageous Description of Short Fatigue Crack Growth Rates in Austenitic Stainless Steels with Distinct Properties

In this work two approaches to the description of short fatigue crack growth rate under large-scale yielding condition were comprehensively tested: (i) plastic component of the J-integral and (ii) Polák model of crack propagation. The ability to predict residual fatigue life of bodies with short initial cracks was studied for stainless steels Sanicro 25 and 304L. Despite their coarse microstructure and very different cyclic stress–strain response, the employed continuum mechanics models were found to give satisfactory results. Finite element modeling was used to determine the J-integrals and to simulate the evolution of crack front shapes, which corresponded to the real cracks observed on the fracture surfaces of the specimens. Residual fatigue lives estimated by these models were in good agreement with the number of cycles to failure of individual test specimens strained at various total strain amplitudes. Moreover, the crack growth rates of both investigated materials fell onto the same curve that was previously obtained for other steels with different properties. Such a “master curve” was achieved using the plastic part of J-integral and it has the potential of being an advantageous tool to model the fatigue crack propagation under large-scale yielding regime without a need of any additional experimental data.

The Evaluation of Front Shapes of Through-the-Thickness Fatigue Cracks

Fatigue failure of structural components due to cyclic loading is a major concern for engineers. Although metal fatigue is a relatively old subject, current methods for the evaluation of fatigue crack growth and fatigue lifetime have several limitations. In general, these methods largely disregard the actual shape of the crack front by introducing various simplifications, namely shape constraints. Therefore, more research is required to develop new approaches to correctly understand the underlying mechanisms associated with the fatigue crack growth. This paper presents new tools to evaluate the crack front shape of through-the-thickness cracks propagating in plates under quasi-steady-state conditions. A numerical approach incorporating simplified phenomenological models of plasticity-induced crack closure was developed and validated against experimental results. The predicted crack front shapes and crack closure values were, in general, in agreement with those found in the experimental observations.

3D assessment of surface influence on crack initiation in sharp notches under a mixed mode of loading

Sharp notches occur in constructions and lead to stress concentrations. Thus they are dangerous points of constructions and must be properly evaluated. In the present study the effect of a free surface on crack initiation conditions is observed and evaluated by means of a 3D model of a specimen with a sharp notch and by means of the finite fracture mechanics of general singular stress concentrators (GSSCs). The effect of a free surface on crack propagation and the crack front shape is described in many publications (Hutař et al., 2010; He et al., 2016; Oplt et al., 2019). Concerning GSSCs (sharp notches, bi-material notches, sharp material inclusions, etc.) crack initiation conditions can also be influenced by the presence of the free surface. In our study we suppose the case of a sharp notch in a homogeneous material with a straight notch front perpendicular to the free surface. In this case a crack can be initiated either from the central region of the notch front or at the vertex point (the point where the notch front intersects the free surface). In order to assess the crack initiation conditions in the 3D model, the critical quantity criterion is employed (Klusák et al., 2019). This criterion can be easily used with the knowledge of basic material parameters and with the use of results of finite element calculations of the assessed notch. It is shown that the place of crack initiation depends on the direction of external loading and thus on a mixity of normal and shear modes of loading. A comparison of results of 2D and 3D models is discussed.

Influence of shape of weld toe and hardness of weld metal on fatigue properties in GMA welded fillet lap joint of UHSS sheet

ABSTRACT This study aims to clarify the influence of shape around weld toe and hardness of weld metal on fatigue crack life in fillet lap joints for automotive chassis elements. Gas metal arc (GMA) welding was performed using 980 MPa class hot rolled steel sheet as the test material. The shape around weld toe and hardness of weld metal were changed by the combination of the shield gas composition and the welding wire. The smoothing of the weld toe significantly improved the fatigue life compared to the hardened weld metal. The total fatigue life was separated into crack initiation life and crack propagation life by measuring the decreasing ratio in the stiffness of the specimen during the fatigue test. Then, the effect of smoothing the weld toe and hardening the weld metal on each life was examined. The changes in the propagating crack front shape and the propagation rate during fatigue test were examined by the beach mark technique. As a result, it was suggested that the smoothing of weld toe improves not only the crack initiation life but also the propagation life by delaying the crack propagation rate in the early stage of crack propagation. The mechanism of retardation of crack propagation rate due to smoothing of weld toe was discussed from the viewpoint of crack shape and aspect ratio.

Experimental Study on the Fatigue Crack Growth and Overload Effect in Medium Density Polyethylene

The fatigue crack growth behavior of medium-density polyethylene (MDPE) under constant amplitude load was experimented on plate specimens. The effect of additional imposed single overload was also researched. An optimized crack front marking method was developed to obtain the actual crack front shape of polymer materials in fatigue crack growth, which was successfully applied to the studied MDPE. The results showed that the retardation of fatigue crack growth evidently appeared after the tensile overload was applied, which was similar to metallic materials. The passivation of the wedge-shaped plastic zone was a primary cause to crack retardation. The theory based on residual stress was introduced to describe the retardation effect, and the plastic zone size of crack tip was calculated by the Dugdale model. The Wheeler model was successfully used to fit the decreased crack growth rate.