Nonlinear Damage Accumulation Research Articles

Modelling creep-fatigue behaviours using a modified combined kinematic and isotropic hardening model considering the damage accumulation

The low cycle fatigue and low cycle fatigue-creep behaviours of P92 steel with strain-control mode and fully inverse loading waveforms at the temperature of 630 °C were investigated. A typical cyclic softening behaviour of P92 steel was observed. As the hold time was introduced at the tensile peak and compressive valley strains, the failure cycle was reduced and the stress reduction became more obvious with the increasing hold time because of the improvement in creep deformation. Moreover, a modified combined kinematic and isotropic hardening model by introducing a non-linear interaction damage accumulation constitutive model was proposed to capture the loop stress-strain behaviour until fracture and predict the failure life as the applied strain amplitudes and duration periods changed. The validation results showed that the accelerated cyclic softening and the greatly reduced failure cycle as the duration periods prolonged under the low cycle fatigue-creep interaction conditions were well described by the modified model.

Nonlinear fatigue damage accumulation: Isodamage curve-based model and life prediction aspects

Cumulative fatigue damage analysis and life prediction of engineering structures/components is vital for ensuring their structural integrity and operational reliability under variable amplitude loadings. In this regard, a new nonlinear fatigue damage accumulation model is proposed by introducing a damage function related to the isodamage curves and remaining life aspects. Specifically, its damage exponent is refined by considering effects of loading history. Experimental data from tests available in literature are utilized for model validation and comparison. Compared with four existing models, the proposed model shows higher precision for cumulative damage modelling and fatigue life prediction than others. Moreover, it improves the deficiencies inherent in other rules under the promise of maintaining its simplicity in practice.

An experimental methodology to characterise post-necking behaviour and quantify ductile damage accumulation in isotropic materials

The development of ductile damage, that occurs beyond the point of necking in a tensile test, can be difficult to quantify. An experimental methodology has been developed to accurately characterise the post-necking deformation response of a material through continuous monitoring of the specimens shape up until rupture. By studying the evolution of the neck geometry, the correct values of the local stress and strain have been determined in samples of grade 304L stainless steel and C110 copper. Notched bar specimens of various notch acuities were examined enabling the effects of stress triaxiality on ductile fracture to be determined. The methodology developed has provided a robust framework for macroscopic measurements of ductile damage during the necking process. To characterise the material degradation process, the elastic modulus reduction method was employed on hourglass-shaped specimens of the same materials. Stiffness degradation was measured using a small gauge extensometer during uninterrupted tensile tests with partial elastic unloadings. A metallographic study was conducted on progressively damaged specimens in order to validate the macroscopic damage measurements. A new non-linear ductile damage accumulation law has been developed and calibrated, which provides an advanced representation of the experimental results, and a significant improvement compared to linear accumulation models frequently employed. This realistic modelling approach considers the degradation of the material when it has undergone severe plastic deformation, and provides a more accurate representation of the near failure behaviour by considering the effects of stress triaxiality. The methodology provides accurate data for damage model development and calibration, to improve the predictions of remnant life from ductile damage in engineering components.

On dynamic behavior of bone: Experimental and numerical study of porcine ribs subjected to impact loads in dynamic three-point bending tests

This study covers the characterization of the dynamic behavior of isolated porcine ribs based on experimental and numerical approaches. A Split Hopkinson Pressure Bar (SHPB) setup for three-point bending tests was used. Data of 20 tests were considered to be comprehensible for experimental characterization, thereby, showing an influence of strain rate on both time for fracture and amplitudes of force response. A three-dimensional porcine rib model was generated from the DICOM (Digital Imaging and Communication in Medicine) images of High-Resolution peripheral Quantitative Computed Tomography (HR-pQCT) scans. Material properties having been fitted by power law regression equations based on apparent density were assigned to the numerical rib. A modified elastic-plastic constitutive law, capable of considering the effects of strain rate was adopted. An incremental and stress-state dependent damage law, capable of considering effects of strain rate on fracture propagation, non-linear damage accumulation and instabilities was coupled to the constitutive law. The Finite Element (FE) model shows high efficiency in predicting both force-displacement curve and the fracture patterns of tested ribs. Predictions prove the ability of the proposed model to investigate the fracture behavior of human ribs under dynamic loads.

Nonlinear Damage Accumulation Rule for Solder Life Prediction Under Combined Temperature Profile With Varying Amplitude

Due to a mismatch of the coefficient of thermal expansion, electronic solder joints experience cyclic shear strain, which ultimately leads to fatigue failure. Traditional predictions of solder joint thermal fatigue life that use the experimental data or the physics-of-failure model often assume a regular profile. For complex temperature profiles, the linear accumulation rule is typically used to integrate the superposition effect. However, the linear rule was proved not applicable to most of the complex loading or temperature conditions. Based on the damage curve theory and the fatigue crack propagation theory, a novel nonlinear accumulation rule has been deduced for solder joint life predictions under irregular profiles, which were composed of two standard temperature cycles and may be experienced by phased-mission system. Four groups of experiments were conducted for ball grid array package solder joints with different dimensions and materials to determine parameters of the proposed nonlinear accumulation rule. The finite-element simulation method was used to extend this rule to more general cases for application. Compared to Miner’s linear accumulation rule, prediction of solder joint thermal fatigue life via the proposed nonlinear accumulation rule is closer to the accelerated life test results of real-world electronic solder joints under a combined temperature profile.

Modelling of nonlinear damage accumulation for the lifetime prediction of adhesively bonded joints

AbstractTwo enhancements of a continuum damage mechanics model with a creep and fatigue part are presented in order to capture nonlinear damage accumulation of structural adhesive joints subjected to service loading. The enhancements are applied to the fatigue part and have an effect on its lifetime prediction due to variable amplitude loading, while its prediction for constant amplitude loading is not affected. Both approaches are validated by means of the comparison of test data with numerical lifetime predictions for shear loading with variable amplitudes.

RETRACTED: Reliability analysis of mechanical components based on a nonlinear fatigue damage accumulation model

The dynamic reliability models of mechanical components with the failure mode of fatigue are mainly based on the linear damage accumulation theory, which is also called the Miner’s rule. But the Mi...

Nonlinear fatigue damage accumulation and life prediction of metals: A comparative study

AbstractFatigue damage modelling and life prediction of engineering components under variable amplitude loadings are critical for ensuring their operational reliability and structural integrity. In this paper, five typical nonlinear fatigue damage accumulation models are evaluated and compared by considering the influence of load sequence and interaction on fatigue life of P355NL1 steels. Moreover, a new nonlinear fatigue damage accumulation model is proposed to account for these two effects. Experimental datasets of pressure vessel steel P355NL1 and four other materials under two‐block loadings are used for model comparative study. Results indicate that the proposed model yields more accurate fatigue life predictions for the five materials than the other models.

A Lattice-Misfit-Dependent Damage Model for Non-linear Damage Accumulations Under Monotonous Creep in Single Crystal Superalloys

A lattice-misfit-dependent damage density function is developed to predict the non-linear accumulation of damage when a thermal jump from 1050 °C to 1200 °C is introduced somewhere in the creep life. Furthermore, a phenomenological model aimed at describing the evolution of the constrained lattice misfit during monotonous creep load is also formulated. The response of the lattice-misfit-dependent plasticity-coupled damage model is compared with the experimental results obtained at 140 and 160 MPa on the first generation Ni-based single crystal superalloy MC2. The comparison reveals that the damage model is well suited at 160 MPa and less at 140 MPa because the transfer of stress to the γ′ phase occurs for stresses above 150 MPa which leads to larger variations and, therefore, larger effects of the constrained lattice misfit on the lifetime during thermo-mechanical loading.

Defect stabilization and reverse annealing in ZnO implanted with nitrogen at room and cryogenic temperature

Despite the fact that nitrogen is a potential acceptor dopant and one of the most studied elements in ZnO, lacking understanding of associated defects and their thermal evolution limits realization of reliable p-type doping of ZnO. Here, we use ion implantation to introduce N at room temperature (RT) and 15 K in ZnO samples with/without a pre-existing buried disorder layer formed by Ag ion bombardment aligned along the [0001] direction. The buried layer contains a high concentration of extended defects, which act as traps for migrating point defects. Channeling analysis shows that reverse annealing occurs in all the N implanted samples during post-implant heat treatment above 600 °C with strong non-linear additive damage accumulation in the co-implanted samples. The reverse annealing effect is less stable in the RT co-implanted sample and the data suggest that a high local concentration of intrinsic point defects, like Zn interstitials, promotes the stability of the N-defect clusters responsible for the reverse annealing. This suggestion is also corroborated by enhanced and defect-mediated Ag outdiffusion at 1100 °C in the RT co-implanted samples.

Nonlinear damage accumulation of concrete subjected to variable amplitude fatigue loading

Nonlinear damage accumulation of concrete subjected to variable amplitude fatigue loading

A Non-Linear Model for Corrosion Fatigue Lifetime Based on Continuum Damage Mechanics

Many structures, such as oil platforms and wind turbines, are built in the marine environment. These structures do not merely suffer from variable cyclic loading due to wind, waves and current, but also from corrosion. Their interaction can give rise to corrosion fatigue, thus reducing the service life and integrity of the structure. The research community witnesses a challenge to identify damage mechanisms of combined fatigue loading and corrosion, and to link this to the lifetime prediction of offshore structures. In this paper, a non-linear corrosion fatigue model is proposed to describe damage accumulation based on continuum damage mechanics. Fatigue endurance limit, load frequency and corrosion rate are included in the model as basic parameters which influence the interaction between fatigue and corrosion. A sequential load effect is revealed via integration of the non-linear accumulation of damage. Parametric studies are conducted to show the abilities of the model. Preliminary simulation results agree to a strong extent with experimental data in the form of corrosion fatigue S-N curves. Nonetheless, deviations are observed at lower life times and these are prone to further investigation. In the future, parameters will be calibrated and further validation experiments will be performed.

Fatigue Damage Mechanism-Based Dependent Modeling With Stochastic Degradation and Random Shocks

This paper proposes a dependent modeling method for reliability estimation of metal structures under constant amplitude loading and random shocks considering the nonlinear damage accumulation mechanism. It is well known that a large monotonic plastic zone ahead of a crack tip caused by a spike overload will retard subsequent fatigue crack growth. However, most existing degradation-and-shock dependent models cannot account for this retardation phenomenon. Moreover, the increase in damage caused by shock is usually assumed to be independent of fatigue degradation. In this investigation, both fatigue degradation and applied random shock damage are considered to have a coupled effect on the crack propagation process. The nonlinear damage superposition approach is utilized herein to model the interaction between fatigue loading and random shocks. Fatigue degradation is considered as a stochastic process influenced by the uncertainties in material properties, and the applied shocks are regarded as random incidents. Next, the piecewise deterministic Markov process is employed to describe the coupling relationship between this stochastic degradation and the random shock process. In the proposed algorithm, Paris’ equation is utilized to describe fatigue degradation, and the Willenborg model is employed to describe retardation caused by random shock loads. A simulation is performed to validate the proposed method, and the proposed method is compared with the traditional method.

Study on the fatigue life and damage accumulation of a compressor blade based on a modified nonlinear damage model

AbstractComparing with the fatigue test results of Ti‐6Al‐4V, the widely used Chaboche damage model shows considerable differences in fatigue life prediction under asymmetric load, which is potentially caused by the local plastic deformation. In this paper, a modified nonlinear damage accumulation model is developed to improve the prediction accuracy for asymmetric loading condition. To account for the elastic and plastic strains, an elastoplastic fatigue factor is developed with 2 weighting factors based on the Ramberg‐Osgood equation and introduced into the stress term of the damage model. The validation of the proposed damage model is verified against the experimental data of Ti‐6Al‐4V titanium alloy and 2024‐T3 aluminium alloy with various stress ratios. Comparing with the original Chaboche model, the predicted life of the proposed model shows much better agreement with the experimental results. Then, the proposed model is used to estimate the fatigue life of a compressor blade of aero‐engine. Considering the variable amplitude loads and the loading sequence, the damage accumulation and the fatigue life of the blade are calculated, and the results indicate a longer fatigue life with slower damage accumulation rate in the early life stage.

Lode dependent plasticity coupled with nonlinear damage accumulation for ductile fracture of aluminium alloy

The experimental program was designed and proportional tests carried out at a room temperature on aluminium alloy 2024-T351. These concerned tension, torsion and compression, in order to investigate the damage accumulation nonlinearity and to reliably calibrate new phenomenological ductile fracture criterion. This fracture model, KHPS2, expressed through the fracture strain, was dependent on the stress triaxiality and normalized third invariant of deviatoric stress tensor. The ductile fracture model was then coupled with the yield criterion, as in the continuum damage mechanics, using the material softening. The plasticity model was considered in the form of taking into account the Lode dependence for investigated material, through normalized third invariant of deviatoric stress tensor. The whole approach, fully applicable to multiaxial ductile fracture related problems, was implemented using the user subroutine into the commercial software, based on the explicit finite element method. In the end, the proposed approach was verified using chosen realized fracture tests, which were used in the calibration, and newly designed KHPS2 criterion along with an existing one—modified Hosford–Coulomb model. The latter model showed better performance in simulations despite worse approximation ability, which can be attributed to its micromechanically-motivated formulation.

A Continuum Damage Mechanics Model for the Static and Cyclic Fatigue of Cellular Composites.

The fatigue behavior of a cellular composite with an epoxy matrix and glass foam granules is analyzed and modeled by means of continuum damage mechanics. The investigated cellular composite is a particular type of composite foam, and is very similar to syntactic foams. In contrast to conventional syntactic foams constituted by hollow spherical particles (balloons), cellular glass, mineral, or metal place holders are combined with the matrix material (metal or polymer) in the case of cellular composites. A microstructural investigation of the damage behavior is performed using scanning electron microscopy. For the modeling of the fatigue behavior, the damage is separated into pure static and pure cyclic damage and described in terms of the stiffness loss of the material using damage models for cyclic and creep damage. Both models incorporate nonlinear accumulation and interaction of damage. A cycle jumping procedure is developed, which allows for a fast and accurate calculation of the damage evolution for constant load frequencies. The damage model is applied to examine the mean stress effect for cyclic fatigue and to investigate the frequency effect and the influence of the signal form in the case of static and cyclic damage interaction. The calculated lifetimes are in very good agreement with experimental results.

On the applicability of Miner’s rule for multiaxial fatigue life calculations under non-proportional load histories

Fatigue design routines and computer codes must use some damage accumulation rule to deal with variable amplitude loadings (VAL), usually Palmgren-Miner (or Miner’s) linear rule for lack of a clearly better option. Nevertheless, fatigue lives are intrinsically sensitive to the order of VAL events, which may e.g. induce residual stresses and thus change the critical point stress state, much affecting its subsequent residual life. On the other hand, in general, non-linear damage accumulation rules are not robust, resulting in better predictions than Miner’s rule only for some specific load orders, requiring a case-by-case analysis. Therefore, Miner’s linear damage rule still is the usual choice in practical fatigue calculations and assessments, giving reasonable predictions at least when properly combined with approaches that sequentially consider plasticity-induced effects, following the critical point stress/strain history in a cycle-by-cycle basis. In this work, Miner’s rule is evaluated for non-proportional tension-torsion loadings on annealed tubular 316L stainless steel specimens. Normal-shear strain histories following either cross, diamond, circular or square paths are applied, and their fatigue lives are measured. Then, more complex VAL paths consisting of combinations of these individual path shapes are applied in other specimens, whose associated fatigue lives are predicted based on Miner’s rule.

A new fatigue damage accumulation model considering loading history and loading sequence based on damage equivalence

In this study, a new nonlinear fatigue damage accumulation model is proposed to consider the effects of loading history and loading sequence under multi-level stress loading based on the Miner–Palmgren rule and S-N curve. By using damage equivalence, the new model is simplified and another form of the model is given. This model improves the application of the traditional Miner–Palmgren rule, by considering not only the loading sequence effect but also the loading history effect. The methods for calculating the degree of safety of specimens and cumulative damage of low-amplitude loads are also presented. Applicability of the new model is validated by predicting the fatigue life of 16Mn and 45 steel specimens under two-level stress loading. Further validation is carried out for the case of 41Cr4 and Aluminum alloys 6082 T6 under multi-level stress loading, and the strengthening and damaging effect of low-amplitude loads is considered. Comparing with the Miner–Palmgren rule and some new models, this new model gives more accurate and reliable prediction.

Numerical prediction of failure in single point incremental forming using a phenomenological ductile fracture criterion

Besides the high simplicity and flexibility, excessive thinning of the sheet metal is one of the limitations of single point incremental forming (SPIF). To overcome this drawback, a finite element (FE) simulation can be implemented for determination of an appropriate deformation strategy. Since the formability in SPIF is often limited by fracture failure, the prediction of ductile fracture using a FE simulation is of the significant importance. In this paper, by implementing the phenomenological modified Mohr-Coulomb (MMC3) model through an appropriate user subroutine within the commercial FE code Abaqus/Explicit, the ductile fracture in SPIF is investigated. Based on the designed tensile tests, the MMC3 criterion is calibrated for AA6061-T6 aluminum alloy sheet using an inverse approach. The stress and strain states of the localized deformation field in SPIF are comprehensively analyzed. With the aid of stress triaxiality and normalized Lode angle parameter, it is shown that the loading path in SPIF is highly nonlinear. Accordingly, a nonlinear damage accumulation rule is utilized to predict the onset of fracture. The comparison of predicted fracture depths of SPIF parts with experimental ones demonstrates an average discrepancy of 10% for utilizing the MMC3 criterion. A good agreement of the fracture location can also be found between experiments and FE simulations. Numerically computed fracture strains show that the fracture forming limit diagram (FFLD) under a proportional loading, like a tensile test, differs in shape and value from the one obtained under a non-proportional loading like SPIF in which the FFLD is higher.

Investigation of Cumulative Fatigue Damage Through Sequential Low Cycle Fatigue and High Cycle Fatigue Cycling at High Temperature for a Type 316LN Stainless Steel: Life-Prediction Techniques and Associated Mechanisms

Cumulative fatigue damage under sequential low cycle fatigue (LCF) and high cycle fatigue (HCF) cycling was investigated at 923 K (650 °C) by conducting HCF tests on specimens subjected to prior LCF cycling at various strain amplitudes. Remnant HCF lives were found to decrease drastically with increase in prior fatigue exposure as a result of strong LCF–HCF interactions. The rate of decrease in remnant lives varied as a function of the applied strain amplitude. A threshold damage in terms of prior LCF life-fraction was found, below which no significant LCF–HCF interaction takes place. Similarly, a critical damage during the LCF pre-cycling marking the highest degree of LCF–HCF interaction was identified which was found to depend on the applied strain amplitude. In view of the non-linear damage accumulation behavior, Miner’s linear damage rule proved to be highly non-conservative. Manson’s damage curve approach, suitably modified, was found to be a better alternative for predicting the remnant HCF life. The single constant (β) employed in the model, which reflects the damage accumulation of the material under two/multi-level loading conditions is derived from the regression analysis of the experimental results and validated further.