Nonlinear Damage Accumulation Rule Research Articles

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.

Characterization of forming limits at fracture for aluminum alloy 6K21-T4 sheets in non-linear strain paths using a biaxial tension/shear loading test

A good knowledge of forming limits at fracture (FLF) for aluminum sheets exhibiting poor formability at room temperature in various non-linear strain paths (N-LSPs) is essential for fully exploiting their forming ability and avoiding their fracture failure. However, the FLF over a wide range of strain states in N-LSPs with pre-strain paths between uniaxial tension and simple shear cannot be determined through the existing two-stage loading test methods. To solve the problem and fill the gap, a new two-stage loading test method employing an optimized butterfly specimen is proposed in this paper, in which strain path changes are controlled by changing biaxial loading conditions acting on the specimen. To validate the capability of the new test method to characterize the FLF in the N-LSPs and investigate the effect of the loading path changes on aluminum 6K21-T4 sheet formability at fracture, different proportional and non-proportional loading experiments using the butterfly specimen obtained from the aluminum sheets are performed. Experimental results indicate that the forming limit strains at fracture over a wide scope of strain states in the N-LSPs can be effectively determined by utilizing the proposed method, thus filling the gap mentioned above. Additionally, four newly developed ductile fracture criteria (a new model proposed in this paper, Hu−Chen 2017, Lou−Huh 2012 and MMC3) together with a non-linear damage accumulation rule (N-LDAR) are employed to forecast the FLF for the 6K21-T4 sheets in the N-LSPs. The results show that both the proposed new model with the N-LDAR and the Hu−Chen model along with the N-LDAR can provide the highest prediction accuracy for the FLF in the N-LSPs. However, the prediction accuracy of the proposed model is much higher that of the Hu−Chen 2017 model for aluminum alloy 5083-O sheets.

Modeling of ductile damage evolution in roll forming of U-channel sections

Abstract In this study, the modified Mohr-Coulomb (MMC) ductile fracture criterion was employed to investigate the ductile fracture during the roll forming process of the AA6061-T6 aluminum alloy. To this aim, the MMC fracture criterion was calibrated based on the tension tests and was integrated into the commercial finite element (FE) Abaqus/Explicit using an appropriate user subroutine. The experimental procedures were designed based on two distinct forming strategies, namely single-stage and multi-stage roll forming processes. The results indicate that the calibrated fracture model based on tension tests is capable to predict the fracture initiation in the single-stage roll forming process at an error rate of 4.47%. Meanwhile, the numerically predicted fracture initiation during the multi-stage roll forming process is inconsistent with the experiments. Hence, a nonlinear damage accumulation rule together with the additional test (multi-stage L-bending) was utilized to predict the onset of fracture throughout the multi-stage roll forming process, considering the effect of deformation mechanics and nonlinear loading path during the process. The results reveal that the fracture onset during the multi-stage roll forming process can be accurately predicted when the MMC fracture criterion with the nonlinear damage accumulation rule is used in the numerical fracture model (with an error of about 9%).

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.

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.

Cumulative Fatigue Damage: CDM-Based Engineering Rule and Life Prediction Aspect

Cumulative fatigue damage analysis plays a key role in life prediction of elements and structures subjected to field loading histories. A general methodology for fatigue life prediction of metallic materials under variable amplitude loading is proposed in this paper. A novel theory of cumulative fatigue damage is presented. It is based on Continuum Damage Mechanics approach which relates the damage rate to that of cyclic loading through the damage function. A new damage function related to isodamage lines and remaining life aspects is analyzed. The final result is a nonlinear fatigue damage rule. The nonlinear damage accumulation rule proposed in this paper improves the deficiencies inherent in other rules and still maintains its simplicity in the application. The relationship with other formulations is pointed out together with the advantages of the proposed model. A number of fatigue damage rules can be derived as a special case of the model developed herein. A wide range of fatigue data available in the literature as well as from the laboratory are used to validate the proposed rule. The agreement between prediction and experiment is found to be excellent. The prediction results are also compared with existing fatigue rules.

Ductile fracture of aluminum 2024-T351 under proportional and non-proportional multi-axial loading: Bao–Wierzbicki results revisited

The effect of stress state and loading path on the ductile fracture of aluminum 2024-T351 is characterized through tension–torsion experiments on tubular specimens. The experimental program includes proportional and non-proportional loading paths leading to the onset of fracture at nearly plane stress conditions at stress triaxialities between 0 and 0.6. Stereo digital image correlation is used to measure the displacements and rotations applied to the specimen shoulders. An isotropic non-quadratic Hosford plasticity model with combined Voce–Swift hardening is used to obtain estimates of the local stress and strain fields within the specimen gage section. The hybrid experimental–numerical results indicate a higher strain to fracture for pure shear than for uniaxial tension. The calibration of a Hosford–Coulomb fracture initiation model suggests that the ductility of aluminum 2024-T351 decreases monotonically as a function of the stress triaxiality, whereas it is a non-symmetric convex function of the Lode angle parameter. It is shown that a simple non-linear damage accumulation rule can describe the effect of non-proportional loading on the strain to fracture.

Efficient Methods for Time-Dependent Fatigue Reliability Analysis

Two efficient methods for time-dependent fatigue reliability analysis are proposed in this paper based on a random process representation of material fatigue properties and a nonlinear damage accumulation rule. The first method is developed by matching the first two central moments of the accumulated damage to a well-known probability distribution, thus facilitating a direct analytical solution of the time-dependent fatigue reliability. The second method uses the first-order reliability method to calculate the reliability index based on a time-dependent limit state function. These two methods represent different tradeoffs between accuracy and computational efficiency. The proposed methods include the covariance structure of the stochastic damage accumulation process under variable amplitude loading. A wide range of fatigue data available in the literature is used to validate the proposed methods, covering several different types of metallic and composite materials under different variable amplitude loading.

Cyclic and Fatigue Behavior of the P355NL1 Steel Under Block Loading

Current fatigue analyses of metallic structures undergoing variable amplitude loading, including pressure vessels, are mostly based on linear cumulative damage concepts, as proposed by Palmgren and Miner. This type of analysis neglects any sequential effects of the loading history. Several studies have shown that linear cumulative damage theories can produce inconsistent fatigue life predictions. In this paper, both fatigue damage accumulation and cyclic elastoplastic behaviors of the P355NL1 steel are characterized using block loading fatigue tests. The loading is composed of blocks of constant strain-controlled amplitudes, applied according to two and multiple alternate blocks sequences. Also, loading composed by blocks of variable strain-controlled amplitudes are investigated. The block loading illustrates that fatigue damage evolves nonlinearly with the number of load cycles, as a function of the block strain amplitudes. These observations suggest a nonlinear damage accumulation rule with load sequential effects for the P355NL1 steel. However, the damage accumulation nonlinearity and load sequential effects are more evident for the two block loading rather than for multiple alternate block sequences, which suggests that the linear Palmgren–Miner rule tends to produce better results for more irregular loading histories. Some phenomenological interpretations for the observed trends are discussed under a fracture mechanics framework.

Analysis of Fatigue Damage under Block Loading in a Low Carbon Steel

Abstract: The fatigue damage accumulation behaviour of the P355NL1 steel is characterised using block loading fatigue tests. First, the constant amplitude low‐cycle fatigue behaviour of the P355NL1 steel is evaluated through strain‐controlled fatigue tests of smooth specimens. Both fatigue and cyclic elastoplastic behaviours are analysed. Then, block loading is applied to identify the key features of the fatigue damage accumulation phenomena for the P355NL1 steel. The block loading is composed of two distinct low‐cycle constant amplitude strain‐controlled blocks. The first block is applied for a predefined number of loading cycles, being followed by a second block which is applied until failure. The block loading illustrates that fatigue damage evolves nonlinearly with the number of load cycles as a function of the strain amplitude. These observations suggest a nonlinear damage accumulation rule with load sequence effects. The linear Palmgren–Miner's rule used extensively in design is not verified for the P355NL1 steel. Finally, using the generated experimental data, the cyclic elastoplastic behaviour of the P355NL1 steel is modelled using a continuum plasticity model with nonlinear kinematic hardening, available in the commercial finite element code ansys®.

Life calculations for materials under irregular nonproportional loading

Experimental data on low-cycle fatigue of 304 steel and a VT9 titanium alloy in deformation by complex loading histories, which are the sequence of blocks of cycles of different shapes in the space of total strains, cited in the literature, are analyzed to develop adequate models for life calculations. The four damage accumulation rules and the low-cycle fatigue deformation criterion were used as basic approaches. Life prediction models were compared. It is shown that the application of a modified nonlinear damage accumulation rule can improve life prediction results, with better outcomes obtained for the programs involving nonproportional cycles.

Stochastic fatigue damage modeling under variable amplitude loading

A general methodology for stochastic fatigue life prediction under variable amplitude loading is proposed in this paper. The methodology combines a nonlinear fatigue damage accumulation rule and a stochastic S–N curve representation technique to achieve this objective. The nonlinear damage accumulation rule proposed in this paper improves the deficiencies inherent in the linear damage accumulation rule and still maintains its simplicity in the application. The covariance structure of the stochastic damage accumulation process under variable amplitude loading is included into the methodology by a new stochastic S–N curve approach. A wide range of fatigue data available in the literature is used to validate the proposed methodology, which covers different type of metallic materials under constant and variable amplitude loadings. The prediction results are also compared with existing fatigue models.

Cumulative Damage Behavior of Anisotropic Al-6061-T6 as a Function of Axial-Torsional Loading Mode Sequence

Two types of low cycle fatigue tests were conducted along two principal orthotropic directions of an orthotropic Al-6061-T6 plate in strain control at room temperature: (1) reference fatigue tests under three loading conditions: push-pull, torsion, and combined push-pull/torsion in-phase; (2) sequential fatigue tests in which different sequences of push-pull and torsion were performed. Fatigue cracking behavior was observed during all of the fatigue tests. Shear cracking dominated the damage of the material. Anisotropic constitutive relations of the material were used in the evaluation of several multiaxial fatigue damage models. The predictive capabilities of these models were assessed based on the results of reference fatigue tests. The damage accumulation behavior of the material was found to depend on the sequence of the loading mode. For the sequence of torsion then push-pull, the damage summation was greater than unity. However, for the sequence of push-pull then torsion, the damage accumulation was near unity as predicted by the linear damage rule. A nonlinear damage accumulation rule could represent the results of the sequential fatigue tests.

Static fatigue of glass-reinforced plastics

Nonlinear damage accumulation rules are usually constructed on the basis of certain hypotheses derived from semiempirical considerations. A method is proposed for constructing an averaged nonlinear damage accumulation rule based on the direct utilization of the results of static fatigue tests on glass-reinforced plastic specimens. Numerical examples of the calculation of the static fatigue strength under repeat loading with a given strength criterion are presented.