Zizi Lu

A simple analytical crack tip opening displacement approximation under random variable loadings

A simple analytical approximation is proposed in this paper to calculate the crack tip opening displacement under general random variable amplitude loadings. This approximation is based on a modified Dugdale model for cyclic loadings. The discussion is first given under constant amplitude loading and is extended to several simple cases under variable amplitude loadings. Following this, a general algorithm is proposed under general random variable loadings. Numerical examples are verified with finite element simulations. Following this, hardening effect is included by including a hardening correction function. The proposed analytical approximation is very efficient compared to the direct finite element simulation. The solution can be used for detailed fatigue crack growth analysis under random variable amplitude loadings.

An incremental crack growth model for multi-scale fatigue analysis

A new fatigue crack growth formulation at the small time scale is proposed in this paper. This method is different from the traditional cycle-based fatigue formulation and is based on the incremental crack growth at any time instant during a cycle. It can be used for fatigue analysis at various time and length scales and is very convenient for the fatigue analysis under random variable amplitude loading without cycle-counting. The proposed model only requires basic material mechanical properties to develop the shape and magnitude of the traditionally used curve. Stress ratio and near-threshold crack growth behavior are included in the proposed methodology. In the proposed methodology, the reversed plastic zone concept and the crack closure concept is adopted to determine the lower integration limit in a single load cycle, respectively. Both approaches have been investigated and their advantages and disadvantages are discussed in detail. The proposed methodology is validated with extensive experimental observations for various metallic materials. Very good agreements with experimental data are observed. Error analysis and statistical testing are employed to compare the accuracy of the crack closure model and the reversed plastic zone model.

Curvilinear Fatigue Crack Growth Simulation and Validation under Constant Amplitude and Overload Loadings

AbstractA concurrent simulation and experimental validation for curvilinear fatigue crack growth (FCG) analysis under both constant amplitude and overload spectrums is proposed in this paper. The simulation methodology is based on a small time-scale fatigue crack growth model and the extended finite element method (XFEM) to calculate the stress intensity factor solution of an arbitrary curvilinear crack. Parametric studies are used to determine the algorithm parameters in the numerical fatigue crack growth simulation. Following this, experimental testing on modified compact specimens is performed under both constant amplitude and overload loadings for model validation. Experimentally measured crack growth orientations and lengths are compared with numerical simulations. Both the experimental and simulation results show the overload retardation behavior for curvilinear cracks under overload loadings. The investigated periodic overload loading has no significant impact on the crack growth orientations. Seve...

General Fracture Criterion for Mixed-mode Delamination in Composite Materials

Interlaminar delamination is one of the most hostile threats to the structural integrity of composite materials. Many failure criteria have been proposed for mixed-mode delamination. Most of existing criteria are not based on underlying failure mechanisms and are obtained through fitting the experimental data from various fracture toughness tests. In this study, a new mixed-mode delamination failure criterion is developed based on a characteristic plane approach and the Tsai-Wu strength theory for composite materials. The proposed failure criterion is based on the different failure mechanisms under pure mode I and mixed-mode loadings. One advantage of the proposed failure criterion is that it only requires two experimental measurements under pure mode I and pure mode II loading and all other mixed-mode failure can be predicted without additional fitting. Verification with extensive experimental data available in the literature is performed to demonstrate the validity of the proposed criterion. A general good agreement is observed between the model predictions and experimental observations. Following this, the proposed new criterion is compared with several existing failure criteria.

Experimental investigation and model analysis of uncertain loading effect on fatigue crack growth

An integrated experimental and simulation approach is proposed to study the effect of loading uncertainties on the fatigue crack growth behavior of Al 7075-T6. Various loading histories, including constant amplitude loadings, single overload block loadings, and deterministic and random variable spectrum loadings are used in the current investigation. Multiple specimen tests are performed and statistical analysis is used to extract the probability distribution of crack size and fatigue life. A previously developed small time scale model is used as a mechanism model to explain the fatigue crack growth behavior under random variable amplitude loadings. Monte Carlo simulation is used for the probabilistic fatigue life prediction. Model predictions are compared with the experimental observations for model validation. It is observed that the effect of uncertain loading is different under different loading spectra. For some cases, the uncertainties of loadings have no major impact on the probabilistic life distribution. For other cases, loading uncertainties have significant impact on the scattering of the life distribution. Model analysis indicates that this behavior is mainly due to the scattering of crack opening stresses produced under different variable amplitude loading spectra.

A small time scale model for creep fatigue crack growth analysis

A novel small time scale model is proposed in this paper for the creep fatigue crack growth analysis. The proposed model is time-based formulation and does not need to transform the realistic loading history to cycles for fatigue analysis. The key idea is to formulate the instantaneous crack growth kinetics with respect to the crack tip opening displacement (CTOD). Creep deformation is included in the CTOD calculation and the effect of frequency/ hold time is intrinsicaly included in the proposed formulation. Crack growth under mechanical and thermal loadings can be directly calculated by the time domain integration according to the specified mechanical and thermal loading history. Various experimental data from the open literature for metals are used to validate the proposed method and a satisfactory agreement is observed.

Small time scale fatigue crack growth analysis under variable amplitude loading

In this paper, a previously developed fatigue crack growth model at the small time scale is modified and validated under f variable amplitude loading. This method is based on the incremental crack growth at any time instant during a cycle and can be used for fatigue analysis at various time and length scales. It does not require cycle counting and is very convenient for the fatigue analysis under random variable amplitude loading without cycle-counting. In the proposed methodology, the reversed plastic zone concept is adopted to determine the lower integration limit during the time integral for crack length calculation. Model validation is performed using extensive experimental observations for various metallic materials under different types of variable amplitude loading. Statistical error analysis is used to compare the proposed model with existing fatigue crack growth codes. Very good agreements are observed between model predictions and experimental observations. Predictions of the proposed model are compared with those of the FASTRAN and AFGROW codes and the error analysis for the predictions indicates the small scale model has an overall better accuracy in the current investigation.