A NEW MULTIPARAMETER APPROACH TO THE PREDICTION OF FATIGUE CRACK GROWTH

A new multiparameter approach is proposed for the prediction of the combined effects of multiple variables on fatigue crack growth. The method, which is based on multiple linear regression analysis, involves the statistical formulation of mathematical expressions for the crack growth rate, da/dN, as a function of multiple variables, e.g. stress intensity factor range, ΔK, crack closure stress intensity factor, K_cl , and stress ratio, R. A general empirical approach is proposed for the estimation of the fatigue crack growth rate as a function of the above variables. The predictive capability of the empirical approach is then verified by comparing predicted and measured fatigue crack growth and crack growth rate data obtained from tests on a quenched and tempered Q1N (HY80) pressure vessel steel. Error ranges and reliability functions are presented within a probabilistic mechanics framework, and the implications of the results are discussed for the development of generalized fatigue life prediction methods.     

A probabilistic multiparameter framework for the modeling of fatigue crack growth in concrete

This paper presents a probabilistic multiparameter framework for the modeling of fatigue crack growth in three grades of concrete. The framework relies on the use of ranked fatigue crack growth rate data (with specified occurrence probability levels) in the formulation of multiparameter fatigue crack growth expressions. These relate ranked fatigue crack growth rates to crack driving force parameters such as the stress intensity factor range, maximum stress intensity factor, stress ratio and occurrence probability level. A probabilistic framework is then presented for the estimation of material reliability or failure probability due to fatigue crack growth. The probabilistic model is then validated for the available data.     

Advanced methodology for assessing distribution characteristics of Paris equation coefficients to improve fatigue life prediction

This paper offers a methodology for coping with information loss following consolidation of data on fatigue crack propagation rates derived from different experiments. It is customary, both in the literature and in standardization, to consolidate results of several experiments conducted under similar conditions, using identical materials. This reduces the ability to implement a probabilistic fracture mechanics approach in order to reliably calculate the distribution of the number of cycles needed to reach a critical value (CV; onset of instability or failure). Such reliable calculation requires, among other things, an estimation of the distribution characteristics of the crack progression curves coefficients represented by models such as Paris or NASGRO, and an estimation of joint distributions of equation coefficients representing such models. Consolidated data reduce the ability to estimate these required distribution characteristics. This work suggests an analytical approach that uses consolidated data, but enables the information to be treated as if it were possible to attribute the data to the various experimental specimens from which they were obtained. Consequently, information required for the evaluation of the distribution of the number of cycles needed to reach a CV can be obtained.
  The proposed approach is generic and can be applied in additional scientific fields that can benefit from separation of data obtained from different experiments.     

Simulation of delamination in composites under high-cycle fatigue

A damage model for the simulation of delamination propagation under high-cycle fatigue loading is proposed. The basis for the formulation is a cohesive law that links fracture and damage mechanics to establish the evolution of the damage variable in terms of the crack growth rate dA/dN. The damage state is obtained as a function of the loading conditions as well as the experimentally-determined coefficients of the Paris law crack propagation rates for the material. It is shown that by using the constitutive fatigue damage model in a structural analysis, experimental results can be reproduced without the need of additional model-specific curve-fitting parameters.     

Probabilistic modelling of safe crack growth and estimation of the durability of structures

Probabilistic models of crack growth are considered at the macro-level of material deformation. These probabilistic models have parameters that can be determined from a fracture mechanics approach. Results from statistical analyses of defects in welded joints show that it is possible to use a two-parameter Weibull distribution as a basic model for the distribution of defect size. On the basis of a Monte Carlo numerical simulation of crack growth, one can construct complete probabilistic diagrams for structural integrity. These diagrams are the basis for designing structures containing defects.     

An engineering approach to fatigue analysis based on elastic‐plastic fracture mechanics

Nowadays cast iron components are widely used in highly stressed structures. Component lifetime is strongly influenced by inhomogeneities caused by the material's microstructure and the manufacturing process (graphite particles, (micro‐)shrinkage pores, inclusions). Inhomogeneities often act as a fatigue crack starter. Lifetime until failure may be divided into stages for crack initiation, short and long crack growth. Initiation of a crack of technical size (a ≈ 1mm) is often dominated by the growth of short cracks. The paper presents an approach to analyse the mechanically short fatigue crack growth based on elastic‐plastic fracture mechanics considering the closure behaviour of short cracks. The effective J‐integral range is used as a crack driving force. Finite element analysis results as well as analytical solutions to approximate the crack driving force are presented. The application of the approach is successfully demonstrated for cast iron material EN‐GJS‐400‐18‐LT using data from fatigue tests, microstructure and fracture surface analyses to assess the fatigue life.     

Probabilistic analysis of the uncertainty in the fatigue capacity of welded joints

This paper presents the results of a study of the uncertainty in the fatigue capacity (constant amplitude fatigue life) of welded steel joints, due to uncertainties related to geometrical and material parameters.An efficient method of probabilistic fracture mechanics analysis is described and applied. A linearelastic fracture mechanics model and the Paris-Erdogan law of crack propagation were adopted. Stressintensity factors were evaluated by employing an influence function method, which is very cost-effective. The main parameters were treated as stochastic variables. Data for weld and crack geometry of the non-load carrying fillet weld cruciform joint selected as the example joint in the study, were recorded from specimens. Other data were compiled from the literature. The uncertainties associated with the basic variables were transformed into a measure of uncertainty of the fatigue capacity by employing the Monte Carlo simulation technique. The relative contributions to the uncertainty in the fatigue capacity from the various factors were also compared.The $\text{S-N}$ data established analytically compared fairly well with test data obtained with 42 specimens. The probabilistic fracture mechanics analysis provided a sufficient sample of data to allow a test of analytical probability distributions to the fatigue life. The fit of two- and three-parameter lognormal and Weibull distributions was examined. Only the three-parameter lognormal pdf passed the chi-square test on the 5% confidence level.     

Modelling the residual strength of fatigue damage at a single semicircular edge notch: Semielliptical crack and through‐the‐thickness crack

In the present paper, computational framework for fatigue performance analysis of a semicircular edge notch with a through‐the‐thickness crack or a semielliptical crack is discussed. The failure behaviour of such configurations is theoretically examined through the stress‐intensity analysis and residual life estimation. The stress field of a damaged notch configuration is herein investigated by employing analytical and numerical approaches. Further, a fracture mechanics–based methodology, developed for fatigue life assessment, is taking into account the crack growth model proposed by Huang and Moan in which the stress ratio is involved. The efficiency of the obtained fatigue damage assessments, related to the edge notch configurations, is verified through appropriate experimental observations.     

Crack initiation and crack propagation under thermal cyclic loading

Theoretical and experimental investigations of crack initiation and crack propagation under thermal cyclic loading are presented. For the experimental investigation a special thermal fatigue test rig has been constructed in which a small circular cylindrical specimen is heated up to a homogeneous temperature and cyclically cooled down under well defined thermal and mechanical boundary conditions by a jet of cold water. At the end of the cooling phase the specimen is reheated to the initial temperature and the following cycle begins. The experiments are performed with uncracked and mechanically precracked specimens of the German austenitic stainless steel X6CrNi 1811.

In the crack initiation part of the investigation the number of load cycles to initiate cracks under thermal cyclic load is compared to the number of load cycles to initiate cracks under uniaxial mechanical fatigue loading at the same strain range as in the cyclic thermal experiment. The development of initiated cracks under thermal cyclic load is compared with the development of cracks under uniaxial mechanical cyclic load.

In the crack propagation part of the investigation crack growth rates of semi-elliptical surface cracks under thermal cyclic loading are determined and compared to suitable mechanical fatigue tests made on compact-tension and four-point bending specimens with semi-elliptical surface cracks. The effect of environment, frequency, load shape and temperature on the crack growth rate is determined for the material in mechanical fatigue tests.

The theoretical investigations are based on the temperature distribution in the specimen, which is calculated using finite element programs and compared to experimental results. From the temperature distribution, elastic and elastic-plastic stress distributions are determined taking into account the temperature dependence of the material properties. The prediction of crack propagation relies on linear-elastic fracture mechanics. Stress intensity factors are calculated with the weight function method and crack propagation is determined using the Paris relation.

To demonstrate the quality of the crack growth analysis the experimental results are compared to the prediction of crack propagation under thermal cyclic load.     

Prediction of creep–fatigue crack growth rates in inert and active environments in an aluminium alloy

This paper reports on a study on creep–fatigue crack growth resistance of a precipitation hardened 2650 T6 aluminium alloy selected for fuselage panels of a future civil supersonic aircraft. The objective is to develop a methodology to predict crack growth under very low frequency loading at elevated temperatures. With this aim, creep crack growth rates (CCGRs), fatigue crack growth rates (FCGRs), creep–fatigue crack growth rates (CFCGRs) have been measured at 130 °C and 175 °C in laboratory air and in vacuum at R = 0.5 under different load frequencies and waveshape signals. It is shown that, for a given temperature, CFCGRs are unaffected by frequency below a critical value of the load period T_c. Above this value CFCGRs are directly proportional to the load period. This time-dependent crack growth regime is assisted by a significant creep damage as indicated by the large amount of intergranular decohesions induced by cavitation on fracture surfaces. CFCGRs are calculated under the assumption that fatigue damage and creep damage can be linearly summed. In vacuum the predictions are in good agreement with experimental data at both temperatures. In air however a discrepancy is observed for low frequency loading, suggesting the occurrence of a creep–fatigue–environment interaction. As a consequence the time-dependent crack growth behaviour affected by this interaction is different from creep crack growth behaviour, although the reasons for this are still unclear. A methodology is then proposed to predict CFCGRs in air. This methodology, if assessed by very low frequency experimental results, could be extended to different structural components made of aluminium alloys operating at elevated temperatures, provided that the mechanisms are unchanged.     

Kurzrisswachstum bei mehrachsig nichtproportionaler Beanspruchung

Short fatigue crack growth under multiaxial nonproportional loading Initiation and short fatigue crack growth have been investigated under nonproportional cyclic loading. A critical plane approach based on fracture mechanics is used for modelling the fatigue process. A Paris‐type crack growth law, formulated using the effective cyclic J‐integral as crack driving force parameter, is integrated to give crack growth curves. Crack opening stresses and strains are calculated with approximation equations. Jiang's plasticity model is used to predict the stress‐strain path. The good agreement between model and real damage evolution is shown comparing experimentally determined crack growth curves, crack orientations, and life curves.     

Fatigue crack growth in double cantilever beam specimen with an adhesive layer

A test method based on fracture mechanics concepts is applied to measure fatigue crack growth rates for an adhesive material in a bondline double cantilever beam specimen containing a cohesive crack. Tension–tension tests are conducted with a stress ratio of 0.5 and at 5 Hz. Debond growth rates are measured using a compliance method. Corresponding changes in J-integral are computed based on the beam on elastic–plastic foundation analysis of the specimen. There are three bondline thicknesses that are evaluated. When computed, ΔJ are plotted against the measured debond growth rates, the results showing a power law relationship which characterizes the debond behavior for a given bondline thickness. The increase of bond line thickness has a significant effect on fatigue crack growth. The larger the bond line thickness, the larger is the fatigue crack growth resistance.     

Fatigue behaviour and life predictions of case-hardened steels

This paper presents experimental and analytical results on fatigue behaviour of case-hardened steel. Fully reversed strain-controlled constant amplitude axial fatigue tests were performed on through-hardened case, through-hardened core and case-hardened steel specimens. Surface versus sub-surface cracking and the role of residual stresses and their relaxation are discussed. Multi-layer models of the case-hardened specimens were used to predict crack nucleation sites as well as fatigue lives, and the predictions corresponded well with the experimental results. Linear elastic fracture mechanics (LEFM) was also used to conduct fatigue crack growth analysis to further explain the experimental observations from the fracture surfaces of the case-hardened specimens. A fatigue strength estimation method based on hardness and inclusion size was used to estimate the fatigue limit of the materials investigated. Fractography of fracture surfaces and crack nucleation location are also presented.     

A stochastic approach to fatigue crack growth in elastic structural components under random loading

Summary A probabilistic analysis of fatigue crack growth, fatigue life and reliability of elastic structural components is presented on the basis of fracture mechanics and the theory of random process. Both the material resistance to fatigue crack growth and the time-history of the stress are assumed to be random. The stress in an elastic structural component is proportional to the corresponding displacement response that is governed either by a linear differential equation for a linear structural system or by a nonlinear differential equation for a nonlinear structural system due to the plasticity other components. Analytical expressions are obtained for the special case that the random stress process is narrow-banded. Numerical examples are given for the randomized Paris-Erdogan type crack growth law to illustrate the procedures and the results are compared with those obtained from simulation to validate the stochastic approach.Dedicated to Prof. Dr. Dr. h. c. Franz Ziegler on the occasion of his 60th birthday     

An improved model for predicting the crack size and plasticity dependence of fatigue crack propagation

The angled crack problem has been given special attention in the recent years by fracture mechanics investigators due to its close proximity to realistic conditions in engineering structures. In this paper, an investigation of fatigue crack propagation in rectangular steel plates containing an inclined surface crack is presented. The inclined angle of the crack with respect to the axis of loading varied between 0° and 90°. During the fatigue tests, the growth of the fatigue crack was monitored using the AC potential drop technique. A series of modification factors, which allow accurate sizing of such defects, is recommended. Paris power law is normalized and adopted for data analysis. Subsequently, this concept is applied to predict crack growth due to fatigue loads. The results obtained are compared with those obtained using the commonly employed fracture criterion and the experimental data.     

A probabilistic static fatigue model for transverse cracking in CFRP cross-ply laminates

This paper presents a delayed-fracture model for transverse cracking in CFRP cross-ply laminates under static fatigue loading. First, a delayed-fracture model for a crack in a brittle material was established on the basis of the slow crack growth (SCG) concept in conjunction with a probabilistic fracture model using the three-parameter Weibull distribution. Second, the above probabilistic SCG model was applied to transverse cracking in cross-ply laminates under static fatigue loading. The stress and the length of the unit element in the transverse layers were calculated with the aid of a shear-lag analysis, taking the residual stress into account. The transverse crack density was expressed as a function of applied stress and time with the parameters in the Paris law and the Weibull distribution function specified, in addition to the mechanical and geometrical properties. Unknown parameters were determined from experiment data gathered in static tensile and static fatigue tests. The reproduced transverse crack density at various applied loads agreed well with the experiment results.     

Modeling of fatigue crack propagation using dual boundary element method and Gaussian Monte Carlo method

This paper studies the modeling of fatigue crack propagation on a multiple crack site of a finite plate using deterministic and probabilistic methods. Stress intensity factor has been calculated by the combined deterministic approach of the dual boundary element method (DBEM) and the probabilistic approach of the Gaussian Monte Carlo method. The Gaussian Monte Carlo method has been incorporated to simulate the random process of the fatigue crack propagation. A finite plate of aluminum alloy 2024-T3 with a thickness of 1.6 mm and 14 holes is analyzed and the fatigue life of the plate is predicted by following a linear elastic law of fracture mechanics. The results of fatigue life predicted by DBEM-Monte Carlo method are in good agreement with experimental ones. The same approach is also applied to two other engineering applications of a gear tooth and a bracket.     

Variability in room temperature fatigue life of alpha + beta processed Ti–6Al–4V

The variability in fatigue behavior is often what drives the design of components such as turbine engine blades and disks. These components are critical and must be designed with a very low probability of failure over the lifetime of the system. To meet that design criterion, the lower limit of fatigue life capability is typically used. The challenge is to reliably predict the lower limit of fatigue behavior. This study investigates the fatigue variability of an alpha + beta processed Ti–6Al–4V turbine engine alloy by conducting a statistically significant number of repeated tests at a few conditions. Testing includes three conditions including two maximum stresses, 675 and 635 MPa; and two surface conditions, electropolished and low stress grinding. All tests are constant amplitude with a stress ratio of 0.1. A similar approach has been performed on several other turbine engine material systems often revealing a bimodal behavior. It is proposed that crack propagation using small crack growth data can be used to predict the low life behavior mode and is demonstrated with the Ti–6Al–4V data.