Numerical Determination of Paris Law Constants for Carbon Steel Using a Two-Scale Model

For most engineering alloys, the long fatigue crack growth under a certain stress level can be described by the Paris law. The law provides a correlation between the fatigue crack growth rate (FCGR or da/dN), the range of stress intensity factor (ΔK), and the material constants C and m. A well-established test procedure is typically used to determine the Paris law constants C and m, considering standard specimens, notched and pre-cracked. Definition of all the details necessary to obtain feasible and comparable Paris law constants are covered by standards. However, these cost-expensive tests can be replaced by appropriate numerical calculations. In this respect, this paper deals with the numerical determination of Paris law constants for carbon steel using a two-scale model. A micro-model containing the microstructure of a material is generated using the Finite Element Method (FEM) to calculate the fatigue crack growth rate at a crack tip. The model is based on the Tanaka-Mura equation. On the other side, a macro-model serves for the calculation of the stress intensity factor. The analysis yields a relationship between the crack growth rates and the stress intensity factors for defined crack lengths which is then used to determine the Paris law constants.

Calculation of the Wöhler (S-N) Curve Using a Two-Scale Model

This chapter deals with the initiation of a short crack and subsequent growth of the long crack in a carbon steel under cyclic loading, concluded with the estimation of the complete lifetime represented by the Wöhler (S-N) curve. A micro-model containing the microstructure of the material is generated using the Finite Element Method and the according non-uniform stress distribution is calculated afterwards. The number of cycles needed for crack initiation is estimated on the basis of the stress distribution in the microstructural model and by applying the physically-based Tanaka-Mura model. The long crack growth is handled using the Paris law. The analysis yields good agreement with experimental results from literature.

A PARIS LAW BASED MESH INDEPENDENT NUMERICAL METHODOLOGY FOR THE SIMULATION OF FATIGUE DRIVEN DELAMINATION IN COMPOSITES

Delamination evolution under cyclic loading is one of the most important research topics for the application of composite materials to aerospace, naval, automotive and, in general, transportation fields. Large experimental campaigns are needed to assess the fatigue behavior of Carbon Fiber Reinforced Polymers (CFRPs), which may result extremely time and cost consuming. Nevertheless, composite materials design needs to take into account the evolution of fatigue driven damage. Subsequently, the development of efficient and robust computational finite element methodologies to evaluate progression of delamination in composite structural components subjected to cyclic loading conditions has become relevant. In this paper, a numerical finite element procedure able to simulate the fatigue driven delamination growth is introduced. A Paris-law based cycle jump strategy, combined with the Virtual Crack Closure Technique (VCCT) approach, has been implemented in the commercial Finite Element Code ANSYS MECHANICAL via the Ansys Parametric Design Language (APDL). The main advantages of the proposed numerical procedure, named FT-SMXB, are related to its independence on the time step and element size in the frame of incremental analyses. The procedure has been preliminary validated, in this research study, at coupon level, by comparing the numerical results to literature experimental data on a unidirectional graphite/epoxy Double Cantilever Beam (DCB) specimen. The significant agreement between the obtained numerical results and the literature experimental benchmark data confirms the accuracy and the potential of the proposed methodology.

A Fatigue Crack Growth Model for Type 304 Austenitic Stainless Steels in an Elevated Temperature Air Environment

The American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code, Section XI utilizes reference fatigue crack growth rate (FCGR) curves for flaw evaluations. The current ASME reference curve for austenitic stainless steels in air environments is a Paris-Law relation with a single ΔK exponent that covers the entire ΔK range. Since generation of the model that became the ASME reference curve, extensive additional FCGR testing of Type 304, Type 304L, and Type 304/304L dual-certified stainless steel and the corresponding weld metal has been performed in an elevated temperature air environment. This testing revealed fatigue crack growth (FCG) behaviors that were not adequately captured by the ASME reference curve. In particular, the ASME reference curve failed to capture a flattening of the FCGR curve in the intermediate ΔK range before the FCGRs sharply dropped off as the threshold behavior is approached. Additionally, the FCGR data showed a slight frequency-dependence. Based on this new data, a new FCGR model was generated for Type 304 austenitic stainless steels in air environments between 250°C and 338°C. A tri-linear Paris-Law style correlation was chosen for the updated FCGR model to accommodate both the flattening of the FCGR curve at intermediate ΔK levels and the sharp downturn in the near-threshold ΔK regime. Each of the three branches of the FCGR curve exhibit a different R-ratio dependence, with the near-threshold regime being the most sensitive to changes in the R-ratio.

Fatigue Life of Ni-Based Single Crystal Super-Alloy Specimen with Single Hole

A method of predicting the fatigue life under multiaxis loads based on the Paris law and EIFS was proposed. And the fatigue life under different loading stress and stress ratio were investigated. The results show that when the loading stress increased from 450~800 MPa, the fatigue life decreased from 6762379 to 10056, as well as when the stress ratio increased from 0.1~1, the fatigue life increased from 6762379 to 14932368. It was validated by test eventually. And the fatigue life model presented here agrees well with test results. It is significant to the prediction of turbine of Ni-based single crystal super-alloy material with filming hole.

Online Prognosis of Bimodal Crack Evolution for Fatigue Life Prediction of Composite Laminates Using Particle Filters

Composite materials are extensively used in aircraft structures, wherein they are subjected to cyclic loads and subsequently impact-induced damages. Progressive fatigue degradation can lead to catastrophic failure. This highlights the need for an efficient prognostic framework to predict crack propagation in the field of structural health monitoring (SHM) of composite structures to improve functional safety and reliability. However, achieving good accuracy in crack growth prediction is challenging due to uncertainties in the material properties, loading conditions, and environmental factors. This paper presents a particle-filter-based online prognostic framework for damage prognosis of composite laminates due to crack-induced delamination and fiber breakage. An optimized Paris law model is used to describe the damage propagation in glass-fiber-reinforced polymer (GFRP) laminates subject to low-velocity impacts. Our proposed methodology deduces the jump energy/inflection point online wherein the damage growth switches from rapid degradation to slow degradation. The prediction results obtained are compared with the conventional Paris law model to validate the need for an optimized bimodal crack growth propagation model. The root mean square error (RMSE) and remaining useful life (RUL) prediction errors are used as the prognostic metrics.

The Numerical Analysis of the In-Plane Constraint Influence on the Behavior of the Crack Subjected to Cyclic Loading

The paper presents the influence of in-plane constraints defined by T-stress on the behavior of a crack subjected to cyclic loading. In the analysis, a modified boundary layer model approach was used in which the cohesive model was introduced. In the simulations, the constant maximum value of the stress intensity factor and four levels of T-stress were defined. The model was subjected to ten repeated stress cycles. Based on the results obtained, an analysis of the effect of the in-plane constraint on selected aspects of crack behavior was made. The strong influence of in-plane constraint applied in the model on the crack closure and the fatigue crack growth rate was proven. Since the in-plane constraint described the influence of geometry on the stress field surrounding the fatigue crack tip in real geometry, the results suggested that it is possible to create precise formulae connecting the level of the in-plane constraint with the effective stress intensity factor range and to incorporate the T-stress or Q-stress level in the Paris law.

Structure Fatigue Crack Length Estimation and Prediction Using Ultrasonic Wave Data Based on Ensemble Linear Regression and Paris’s Law

This paper presents methods for the 2019 PHM Conference Data Challenge developed by the team named "Angler". This Challenge aims to estimate the fatigue crack length of a type of aluminum structure using ultrasonic signals at the current load cycle and to predict the crack length at multiple future load cycles (multiple-step-ahead prediction) as accurately as possible. For estimating crack length, four crack-sensitive features are extracted from ultrasonic signals, namely, the first peak value, root mean square value, logarithm of kurtosis, and correlation coefficient. An ensemble linear regression model is presented to map these features and their second-order interactions with the crack length. The Best Subset Selection method is employed to select the optimal features. For predicting crack length, variations of the Paris’ law are derived to describe the relationships between the crack length and the number of load cycles. The material parameters and stress range of Paris’ law are learned using the Genetic Algorithm. These parameters will be updated based on the previous-step predicted crack length. After that, the crack length corresponding to a future load cycle number for either the constant amplitude load case or variable amplitude load case is predicted. The presented methods achieved a score of 16.14 based on the score-calculation rule provided by the Data Challenge committees, and was ranked third best among all participating teams.

Parametric Study of Fatigue Crack Growth in a Finite Plate

Fatigue crack propagation is an undesirable phenomenon that may lead to catastrophic failures in many components and structures, therefore it is important to understand its underlying mechanics. To that effect, systematic parametric studies of fatigue crack propagation laws are interesting to determine how fatigue life varies with the constants that define the mechanical behavior of a given material in a fatigue situation, such as the Paris’ law constants, fracture toughness (Kc) or the stress range ??. The parametric studies performed in the present work assess the influence of several parameters, assuming that failure occurs when K>Kc, but also when all the material ahead of the crack is yielding. It was found that m and C, the Paris’ law parameters, are the most influential parameters in terms of fatigue life. The present study should help future designers when choosing materials for components or structures subjected to cyclic loads.