Damage Mechanics Approach Research Articles

Fatigue damage mechanics approach to predict the end of incubation and breakthrough of leading edge protection coatings for wind turbine blades

The state of the surface of the leading edge of wind turbine blades is important for optimal aerodynamic performance. Rain erosion leads to damage and roughness on the leading edge. In this study, we present an approach to predict the level of roughness of the leading edge based on fatigue damage accumulation due to impacts of rain droplets. Impact simulations of droplets on the protective coating layer are coupled with rain erosion test data and fatigue S-N curves. Fatigue damage values are then related to surface roughness levels. An approach to extract S-N curve parameters from a rain erosion test and then make predictions for other coatings based only on the output of impact simulations is presented and tested against test data. Both the end of incubation and coating breakthrough times are predicted with this approach. Stress, strain and energy density values were used as fatigue damage indicators and the respective predictions were compared to each other. It was found that the maximum principal strain gave the best predictions and matched the experimental trends.

Progressive damage and stiffness degradation assessments of double‐lap CFRP/Ti interference fit bolted joints under quasi‐static tensile load

AbstractMatrix crack propagation and stiffness degradation behaviors of the carbon fiber reinforced polymer/titanium alloy (CFRP/Ti) bolted joint were characterized by a synergistic damage mechanics approach. The parametric study including pre‐tightening torques and interference fit sizes was conducted. The results showed that the joint stiffness degradation exhibited characteristics of local stiffness degradation due to local stress concentration. Stiffness degradation in different plies was caused by matrix crack damage occurring in different directions. The pre‐tightening torque significantly increased the joint stiffness and restrain matrix crack progression, effectively inhibiting the stiffness degradation of the joint. Moreover, the low interference fit level delayed the crack initiation in −45° ply and 45° ply and the crack propagation of the laminate, while promoted the crack initiation in 90° ply. The stiffness degradation of the laminate could be significantly reduced by interference fit.Highlights Matrix crack propagation and stiffness degradation behaviors of the CFRP laminate were characterized by a synergistic damage mechanics method. A FE model of the CFRP/Ti double‐lap interference fit bolted joint was established. Influences of pre‐tightening torques on both matrix crack initiation and propagation were investigated. The optimum interference fit size of the matrix damage strengthening was 0.20%–0.60%.

An extended lumped damage mechanics IGABEM formulation for quasi-brittle material failure

This study proposes a new formulation for the mechanical modeling of quasi-brittle materials. The material degradation due to cracking is addressed through the Extended Lumped Damage Mechanics (XLDM) approach. The model is inserted into an IGABEM formulation, where Non-Uniform Rational B-Splines (NURBS) are the basis functions. A novel nonlinear solution technique has been developed for the numerical implementation. Crack propagation is captured using the initial stress field approach, widely utilized by the BEM community to account for nonlinear material behavior. The XLDM is coupled into an IGABEM formulation by discretizing part of the domain into cells, placed only where damage is expected to grow. Classical benchmark problems are presented to demonstrate the method’s capability and effectiveness. The results show excellent agreement with both experimental and numerical findings from the literature. Damage evolution is assessed through the band thickness opening, leading to material degradation. This method offers a new way of addressing damage mechanics problems within the BEM framework. It could benefit the BEM community, as traditional damage analysis within this numerical method often leads to significant time-consuming and elevated computational costs, which are mitigated by the formulation proposed herein.

Modelling and Characterisation of Orthotropic Damage in Aluminium Alloy 2024.

The aim of the work presented in this paper was development of a thermodynamically consistent constitutive model for orthotopic metals and determination of its parameters based on standard characterisation methods used in the aerospace industry. The model was derived with additive decomposition of the strain tensor and consisted of an elastic part, derived from Helmholtz free energy, Hill's thermodynamic potential, which controls evolution of plastic deformation, and damage orthotopic potential, which controls evolution of damage in material. Damage effects were incorporated using the continuum damage mechanics approach, with the effective stress and energy equivalence principle. Material characterisation and derivation of model parameters was conducted with standard specimens with a uniform cross-section, although a number of tests with non-uniform cross-sections were also conducted here. The tests were designed to assess the extent of damage in material over a range of plastic deformation values, where displacement was measured locally using digital image correlation. The new model was implemented as a user material subroutine in Abaqus and verified and validated against the experimental results for aerospace-grade aluminium alloy 2024-T3. Verification was conducted in a series of single element tests, designed to separately validate elasticity, plasticity and damage-related parts of the model. Validation at this stage of the development was based on comparison of the numerical results with experimental data obtained in the quasistatic characterisation tests, which illustrated the ability of the modelling approach to predict experimentally observed behaviour. A validated user material subroutine allows for efficient simulation-led design improvements of aluminium components, such as stiffened panels and the other thin-wall structures used in the aerospace industry.

Modeling the thermo-oxidative aging effects on fatigue life of natural rubber using a continuum damage mechanics approach

Thermo-oxidative aging (TOA) significantly impacts the fatigue life of rubbers by reducing the fatigue strength and modifying the slope of the Wöhler curve, rendering traditional time-temperature superposition methods inadequate. In this work, we aim to develop a model capable of predicting the effect of TOA on the fatigue properties of rubbers. For this purpose, dumbbell specimens of natural rubber (NR) were subjected to aging in an air-vented oven at different temperatures prior to mechanical testing. Tensile tests were conducted to quantify the aging effects on a microscale network parameter known as elastically active chains (EAC) density, along with determining ultimate properties such as the stress and strain at break. By using a time-temperature equivalence and the Arrhenius shift factor, master curves were constructed for both EAC density and ultimate properties. Subsequently, the fracture properties of the aged material were predicted using an energy limiter approach whose evolution follows that of EAC density. Furthermore, a relationship between the parameters of the continuum damage mechanics (CDM) approach (specifically, the power law parameters of the Wöhler curve) and the fracture properties was proposed, resulting in accurate estimates of the fatigue life regardless of the aging conditions. Satisfactory agreement was observed between the model predictions and the data for nine aging conditions encompassing four different temperatures. The CDM approach also allows assessing the evolution of mechanical damage within the material influenced by TOA. The novelty of this approach lies in establishing a direct relationship between fatigue and fracture properties. Moreover, this is the first time to the best of our knowledge that TOA has been explicitly incorporated into a fatigue life prediction model via the evolution of the EAC density.

Numerical investigation of wellbore damage due to drill string lateral vibration

During drilling operations, cyclic loading is exerted on the wellbore wall by the vibrations of the drill string. This loading could lead to rock fatigue, which in turn might result in wellbore failure. In this study, a numerical model is developed to simulate the effects of repeated loading on rock fatigue and failure. The simulation is based on an elasto-plastic constitutive model coupled with a damage mechanics approach, which allows us to examine the wellbore instability due to drill string vibrations. The model is verified with the existing data in the literature related to experiments on impact of a steel ball against a curved wall. The findings indicate that cyclic loading increases the development of plastic strain around the wellbore significantly compared to static conditions, promoting rock fatigue. Furthermore, the cyclic loading expands the radius of the yielded zone substantially, a critical factor for maintaining wellbore integrity. The proposed model can be used to evaluate the wellbore stability under repetitive loading caused by the drill string action.

Comparative assessment of a continuum damage mechanics-based creep damage models for India-specific RAFM steel

ABSTRACT In the present investigation, a comparative assessment of Kachanov-Rabotnov (KR) and Liu-Murakami (LM) Creep Damage Models is presented for India-Specific Reduced Activation Ferritic Martensitic (IN-RAFM) steel, in the framework of Continuum Damage Mechanics (CDM) approach using ABAQUS finite element analysis software. The assessment is made based on the prediction of entire creep curve and creep rupture life of IN-RAFM steel at 823 K under uniaxial tensile loading at the stress levels of 200–260 MPa. Results disclosed that LM model accurately predicts the rupture life and creep deformation in comparison to KR model and the corresponding R-square values are 0.999 (LM model) and 0.993 (KR model), respectively. The material constant q of LM model controlled the damage evolution in tertiary creep stage. In contrast, the high value of constant ∅ in damage rate equation of KR model, led to over prediction of creep strain owing to high damage rate evolution.

Fatigue Life Prediction for 2060 Aluminium–Lithium Alloy with Impact Damage

The paper investigates the issue of post-impact fatigue damage of the 2060 aluminium–lithium alloy, a representative material of third-generation aluminium–lithium alloys extensively employed in the fuselage of C919 aircraft due to its notable attributes of high specific stiffness and strength. Initial impact damage is identified utilizing a residual stress–strain field obtained from a quasi-static simulation. Then, the continuum damage mechanics approach is applied to predict the fatigue life of the impacted 2060 aluminium–lithium alloy plates accounting for the combined effects of residual stress, plastic damage, and fatigue loading. A comparative analysis between calculated and experimental results is conducted to validate the efficacy of the proposed methodology.

Study on the nonlinear viscoelastic behavior of rubber composites filled with silica

Silica-filled rubber composites exhibit nonlinear viscoelastic behavior depending on filler dispersion and matrix interaction. This study investigated the effects of silane treatment on dynamic mechanical properties of precipitated and fumed silica-reinforced polybutadiene rubber composites. The silane coupling agent improved filler dispersion and interfacial adhesion as characterized by microscopy and bound rubber content. Payne effect measurements showed enhanced storage modulus and network stability for silanized composites due to better filler networking. Cyclic tensile loading displayed reduced stress-softening in treated composites attributable to minimized damage formation. Modeling using Kraus and damage mechanics approaches provided quantitative correlations between the microstructure and magnitude of nonlinear response. The results demonstrate that silane treatment optimizes the viscoelastic performance of silica-filled rubber composites.

A thermodynamically consistent strain difference-based nonlocal damage mechanics approach for failure analysis of quasi-brittle materials

The nonlocal integral approaches are established methods known for their effectiveness in dealing with the challenges of ill-posed behaviour and mesh sensitivity during the strain softening process, especially within classical continuum theories. The present work extends the strain difference-based nonlocal approach to continuum damage mechanics (CDM) theories for predicting the failure behaviour of quasi-brittle materials. The strain difference approach is adopted for two reasons: (i) it maintains physical realism and indirectly incorporates nonlocal effects while computing both the damage variable and the damage energy release rate, and (ii) the constitutive model maintains a symmetry nature in constructing the nonlocal part of the stiffness matrix, reducing the computational cost in strain-softening problems. The state and damage evolution equations for the present nonlocal approach are formulated within the thermodynamic framework. Numerical examples involving 2D and 3D cases are solved: (i) to study the influence of nonlocal parameter ‘α’ on the damage distribution while capturing the post-peak behaviours, (ii) to demonstrate the effectiveness of the present methodology by obtaining mesh-independent results and accurately predicting damage propagation paths, and (iii) to compare the experimental results and numerical structural response for coarse mesh, highlighting both computational efficiency and reduction of mesh-bias dependency. The results obtained by the strain difference-based nonlocal damage model agree well with the experimental results in the literature.

ANALYSIS OF CORD–RUBBER COMPOSITE RESPONSE BY USING THE NONLINEAR CONTINUUM DAMAGE MECHANICS APPROACH

ABSTRACT The phenomenon of damage observed in cord–rubber composite laminates is the result of deformation, heat, chemical damage, and fracture. The micro cracks and the initial voids, present before any load is applied, grow through the mechanism of coalescence and generate permanent macroscopic cracks. A damage approach is proposed to describe the cumulative effects and damage evolution under cyclic loading and thermal and chemical impact. The approach parallels the continuum damage mechanics approach advocated by Kachanov and Rabotnov.1,2 It is a phenomenological model that depends on laboratory testing to describe the evolution of damage and contains one scalar parameter to describe the collective effect of material damage. The following analysis is based on the premise that the cyclic interlaminar shear strain, coupled with the running temperature at the free edge, is the primary cause of damage. The model constants were derived from an alternating stress (S) against the number of cycles to failure (N) (i.e., S-N) curve at room temperature. The temperature effect on the material damage was accounted for by an Arrhenius shift function of the S-N curve. Numerical simulation of a composite laminate was conducted using the user subroutine UMAT in ABAQUS. The results presented reflect the accuracy of the proposed methodology to predict the location of the ensuing damage and the path of the damage propagation.

A 3D objective material model for elastic–plastic damage behavior of fiber reinforced polymer composites

To simulate the plastic deformation and the progressive failure process of fiber reinforced polymer composites under 3D stress conditions, a new elastic–plastic damage model is proposed to satisfy the objectivity of 3D stress conditions. A new two-parameter 3D plasticity criterion and a simple non-associated flow potential, expressed by stress invariants of a transversely isotropic unidirectional (UD) lamina, are developed to characterize plastic deformation in an objective way. Moreover, the material degradation model and damage evolution laws are constructed on a matrix fracture angle-dependent coordinate system to ensure the objectivity of the continuum damage mechanics (CDM) approach. In addition, a new linear law alleviating mesh dependence is derived to govern the damage variable evolution in the elastic–plastic damage process. ​The effectiveness and objectivity of the proposed material model are demonstrated by a series of test cases.

Comparison of the continuum damage and fracture mechanics in fatigue assessment of components containing residual stresses

In the present study, the fatigue crack growth life of standard and smooth notched specimens containing residual stresses are evaluated based on the continuum damage and fracture mechanics approaches. It is indicated that fatigue crack growth lives assessed by the continuum damage model are closer to the experimental results, with a difference of <10% in the specimens containing residual stresses. The total stress intensity factor range is used to consider the effects of residual stresses in the estimation of fatigue crack growth life based on the fracture mechanics. It is found that in existing residual stresses, the stress intensity factor K is not a proper parameter to evaluate crack tip zone. Fatigue crack initiation life is experimentally obtained based on assessing variations of the slope of unloading curve in the force-displacement diagram of fatigue experiments. The cycle including a change in the slope is considered as fatigue crack initiation event. Isotropic and kinematic hardening parameters of ASTM A516 pressure vessel steel are considered in finite element analyses. Tensile residual stresses are introduced into the notched specimens by employing four-point-bending with a magnitude of around 90% of the yield stress of the material. The results indicate that at least 65% of the fatigue life of the specimens is decreased due to the presence of tensile residual stresses. Tensile residual stresses are measured using the hole-drilling technique.

Hierarchical multi-scale analysis of the effect of varying fiber bundle geometric properties on the mechanical properties of 3D braided composites

A hierarchical multi-scale numerical model is developed to predict the effect of cross-sectional geometric properties on the mechanical response of three-dimensional (3D) braided composites. In this model, the effective properties are transferred from the fiber bundle scale to the mesoscale, and the finite element and analytical methods are used to predict the macroscopic mechanical properties. Damage evolution was evaluated, based on a continuous damage mechanics approach. A user-defined material subroutine (UMAT), in a nonlinear finite element analysis, has been developed to implement the proposed model and further determine the response and subsequent damage evolution in 3D braided composites subjected to quasi-static tension. The elastic properties of the composites are predicted using a hybrid multi-scale model. The agreement between the numerical simulations and the experimental results is good. It has been shown that the cross-sectional geometry of the fiber bundle properties has a significant influence on the tensile behavior of the composite, which is captured by the proposed multi-scale damage model. This research offers a theoretical analysis for selecting the optimized fiber bundle geometry for using in FE predictions of 3D braided composites.

Interaction of compression failure mechanisms in composites with ply waviness defects

This article presents results from experimental and computational investigations of composite laminates with embedded ply waviness defects of different geometries under compression. The effect of the ply waviness defect on the initiation, interaction, and evolution of failure mechanisms of surrounding plies are studied. Using high-resolution imaging and digital correlation analysis, the strain localization phenomenon is monitored, and the sequence of failure mechanisms is established. The experimental observations are supported with computational finite element progressive failure analyses of the same composites with ply waviness defects using an energy based continuum damage mechanics approach. For the case of laminates with ply waviness defects of high angles, a delamination crack between the wavy plies and adjacent transverse plies is the dominant mode of failure, which interacts strongly with the fiber compression and matrix tension modes. For the case of laminates with ply waviness defects of low angles, failure does not initiate at the waviness defect but at locations where the laminate strength was locally reduced due to other microstructural defects. The combined experimental and computational analyses presented here advanced the understanding of the interaction of compression failure mechanisms in composites with ply waviness defects, which is highly challenging to experimentally measure.

Cumulative Fatigue Damage of Composite Laminates: Engineering Rule and Life Prediction Aspect.

The analysis of cumulative fatigue damage is an important factor in predicting the life of composite elements and structures that are exposed to field load histories. A method for predicting the fatigue life of composite laminates under varying loads is suggested in this paper. A new theory of cumulative fatigue damage is introduced grounded on the Continuum Damage Mechanics approach that links the damage rate to cyclic loading through the damage function. A new damage function is examined with respect to hyperbolic isodamage curves and remaining life characteristics. The nonlinear damage accumulation rule that is presented in this study utilizes only one material property and overcomes the limitations of other rules while maintaining implementation simplicity. The benefits of the proposed model and its correlation with other relevant techniques are demonstrated, and a broad range of independent fatigue data from the literature is used for comparison to investigate its performance and validate its reliability.

Numerical modelling of microstructure inhomogeneity to reproduce experimentally observed scatter in fretting fatigue lifetimes

Experimental fretting fatigue lives exhibit large degree of scatter. One of the aspects behind this is the microstructural inhomogeneity which affects the stresses in the material. Variance in stress values can greatly impact crack initiation speed, leading to changes in fretting fatigue lifetimes, as well as the crack propagation behaviour. This research aims to study this issue in more detail and recreate the experimentally observed scatter using numerical modelling. In this work, Voronoi tessellation is used to simulate microstructural topologies of low carbon steel, where each grain is assigned elasto-plastic properties at random, from a predetermined range. In total, 60 finite element models are created and the effect of microstructural inhomogeneity on fretting fatigue lifetime dispersion is evaluated using a Continuum Damage Mechanics approach. Additionally, crack propagation is studied with XFEM combined with Smith-Watson-Topper fatigue parameter to determine crack path under multiaxial, non-proportional loading conditions. For both crack initiation and propagation investigation, the Theory of Critical Distances is applied to overcome the effect of high stress gradients. Simulation results show that microstructural inhomogeneity has significant impact on the contact stress distributions and subsurface stress and strain fields. Scatter observed in the predicted lifetimes matches well with that observed in practical experiments and is used to propose a design curve for the studied material. The applied crack path prediction approach captures the variance in crack paths originating from microstructural inhomogeneity and shows good correlation with reference experimental results at low bulk stress levels.

Acceleration mechanism of the degradation of the lifetime of Ni‐based superalloys under creep‐fatigue loading at elevated temperatures

AbstractIn this study, intermittent creep‐fatigue tests were applied on Ni‐based Alloy 617 and Alloy 625. Scanning electron microscope (SEM) observation and electron back‐scatter diffraction (EBSD) analysis were employed to the evaluation of the degradation of the crystallinity under the creep‐fatigue loads. It was found that the initial damage under creep‐fatigue load basically appeared as intergranular cracks. In addition, the lifetimes of Alloy 625 samples fluctuated significantly due to the growth of NbC precipitates. The initial damage of these two alloys was dominated by the growth and accumulation of dislocations and vacancies around the interface that consisted of large lattice mismatch. Local atomic diffusion was activated when the summation of the nominal stress and local stress caused by the large lattice mismatch exceeded a critical value. The stress‐induced acceleration of the degradation of the crystallinity of the alloys was analyzed by applying the modified Arrhenius equation. Instead of the most popular inversion methods according to the final failure mode, the quantitative description in life prediction was developed based on the dynamic progress for acceleration mechanism of the degradation. It is of importance to perfecting the frontiers of damage mechanics approach.

Investigation of creep-fatigue crack initiation by using an optimal dual-scale modelling approach

In this work, three dual-scale modelling approaches containing sub-modelling approach, coupled modelling approach and full-field crystal plasticity finite element (CPFE) approach are implemented for notched structures under creep-fatigue loading conditions. Based on the comprehensive comparisons, the sub-modelling approach is determined to be an optimal simulation strategy among them. Furthermore, the combined effects of grain orientation and stress concentration on crack initiation are investigated by adopting the sub-modelling approach. Under low stress concentration factor, the most potential positions of crack initiation randomly locate at the root of geometric discontinuities owing to the influence of grain orientation distribution. With the increase in stress concentration factor and decrease in the number of grains at hotspots, the cooperative relation between grain orientation and stress concentration factor for creep-fatigue crack initiation is revealed through a sequence of simulation results, followed by the competitive relation. On this basis, a feature region map is constructed to distinguish the factor-dominated crack initiation. Finally, a case study of turbine disk is provided to illustrate the engineering meanings of the dual-scale modelling approach. The link from scientific problem to engineering application for the crack initiation prediction is bridged by the damage mechanics approach, which is also expected to be promoted in many high-temperature components.

Two-Scale analysis of fretting fatigue crack initiation in heterogeneous materials using Continuum Damage Mechanics

The phenomenon of fretting fatigue damage is related to tribological behaviour and commonly occurs at the contact interface between two bodies that sustain oscillation loads. Based on the complicated mechanical situation, several methods have been developed to predict the crack initiation location and life. The Continuum Damage Mechanics (CDM) approach in conjunction with Finite Element Method (FEM) is used in this paper. The fretting fatigue lifetime includes two parts, crack initiation lifetime and crack propagation lifetime, and this paper focuses on the crack initiation phase. Homogeneous materials are usually studied in fretting fatigue problems, and the influence of defects is necessary to be considered. In this study, the authors proposed several models to consider the effect of heterogeneity on crack initiation location and lifetime. The numerical model is a 2D one with plane strain assumption. To get more accurate numerical results with low computational cost, a Two-Scale Analysis approach is developed in this paper. Two macroscopic models and three microscopic models are proposed, including a Macroscopic homogeneous model (Macro-HOMO), a Multiscale Homogenization model with Direct Numerical Simulation (MH-DNS), a Microscopic homogeneous model (Micro-HOMO), a Microscopic Model with equivalent material properties by using Mean Field Homogenization method (Micro-MFH), and a microscopic model with Direct Numerical Simulation (Micro-DNS). The results obtained by using the CDM approach with different microscopic models are compared, and show that the prediction accuracy of the Micro-DNS is the best. In addition, in terms of computational cost, the Micro-DNS model shows great advantages as well comparing to the Macro-DNS model.