Cyclic Crack Tip Opening Displacement Research Articles

An Overview of the mechanism-based thermomechanical fatigue method (DTMF) in the design of automotive components

The DTMF damage Parameter described in the paper is the generalization of the creep fatigue parameter (DCF) proposed by Riedel, which quantifies the amount of damage produced by a non-isothermal loading cycle. The entire design methodology is outlined in the text, starting with the calibration of Chaboche's viscoplastic model and then the determination of the thermomechanical fatigue (TMF) parameters. Chaboche is generally a good choice for its ability to describe well both kinematic and isotropic hardening behaviors, also enabling stress relaxation and strain rate dependency to be considered. The DTMF method is based on the fracture mechanics concept of cyclic crack tip opening displacement (ΔCTOD) where the effective stress range takes the crack closure effect into account. This method is typically used to describe the thermomechanical low cycle fatigue behavior of cast irons, cast steels, stainless steels, Inconel, HiSiMo and nickel-based alloys. These materials are used in components that need to withstand high temperatures (higher than half of the melting point) in service as exhaust manifolds, cylinder heads, valves, turbochargers and disk brakes. Three failure mechanisms are detailed here: oxidation, creep and fatigue. Oxidation is a complex phenomenon that may occur when the material is hot under tensile in-phase loading or hot under compressive out-of-phase loading. Creep is a time and temperature dependent diffusion process which is incorporated into the DTMF parameter as a multiplicative factor. In this context fatigue life is defined as the number of cycles to propagate an existent microcrack up to an arbitrary size that is defined on a case-by-case basis.

ProCrackPlast: a finite element tool to simulate 3D fatigue crack growth under large plastic deformations

Many structural components and devices in combustion and automotive engineering undergo highly intensive cyclic thermal and mechanical loading during their operation, which leads to low cycle (LCF) or thermomechanical (TMF) fatigue crack growth. This behavior is often characterized by large scale plastic deformations and creep around the crack, so that concepts of linear-elastic fracture mechanics fail. The finite element software ProCrackPlast has been developed at TU Bergakademie Freiberg for the automated simulation of fatigue crack growth in arbitrarily loaded three-dimensional components with large scale plastic deformations, in particular under cyclic thermomechanical loading. ProCrackPlast consists of a bundle of Python routines, which manage finite element pre-processing, crack analysis, and post-processing in combination with the commercial software Abaqus . ProCrackPlast is based on a crack growth procedure which adaptively updates the crack size in finite increments. Crack growth is controlled by the cyclic crack tip opening displacement varDelta CTOD, which is considered as the appropriate fracture-mechanical parameter in case of large scale yielding. The three-dimensional varDelta CTOD concept and its effective numerical calculation by means of special crack-tip elements are introduced at first. Next, the program structure, the underlying numerical algorithms and calculation schemes of ProCrackPlast are outlined in detail, which capture the plastic deformation history along with the moving crack. In all simulations, a viscoplastic cyclic material law is used within a large strain setting. The numerical performance of this software is studied for a single edge notch tension (SENT) specimen under isothermal cyclic loading and compared to common finite element techniques for fatigue crack simulation. The capability of this software is featured in two application examples showing crack growth under mixed-mode LCF and TMF in a typical austenite cast steel, Ni-Resist. In combination with a crack growth law identified in terms of varDelta CTOD for a specific material, the tool ProCrackPlast is able to predict the crack evolution in a 3D component for a given thermomechanical loading scenario.

Numerical calculation of [formula omitted] to simulate fatigue crack growth under large scale viscoplastic deformations

Crack propagation under low cycle fatigue and thermomechanical fatigue is characterized by high plastic and creep strains that extend over large regions around the crack, so that concepts of linear-elastic fracture mechanics cannot be applied. In these cases, the cyclic crack tip opening displacement ΔCTOD is a promising loading parameter to quantify crack growth. In this work, suitable definitions and Finite Element techniques are investigated and compared for an accurate calculation of ΔCTOD under cyclic mechanical and/or thermal loading. A viscoplastic temperature dependent material model of Chaboche-type is used along with large strain settings, specified for the austenitic cast iron Ni-resist. Extensive two-dimensional analyses of Single Edge Notch Tension specimens revealed that collapsed special crack tip elements are superior compared with commonly used regular quadrilateral 8-node elements. At the same level of accuracy of ΔCTOD, they require an about ten times coarser mesh and show less sensitivity w.r.t. element size for both stationary and propagating cracks. In order to simulate fatigue crack growth, an efficient, fully automated FE-technique is developed for an incremental crack propagation by successive remeshing, whereby the deformations and internal state variables are mapped from the old mesh onto the new one. Recommendations are made regarding important numerical control parameters like optimal size of crack tip elements, length of crack growth increment in relation to plastic zone size and ΔCTOD value.

Microstructure-sensitive finite-element analysis of crack-tip opening displacement and crack closure for microstructural short fatigue cracks

In this paper, the effect of the polycrystalline microstructure on crack-tip opening displacement and crack closure is investigated for microstructural short plane strain fatigue cracks using the finite-element method. To this end, cracks are introduced in synthetically generated microstructures and the grain properties are described using a single crystal plasticity model with kinematic hardening. Additionally, finite-element calculations without resolved microstructure and von Mises plasticity with kinematic hardening are performed. Fully-reversed strain-controlled cyclic loadings are considered under large-scale yielding conditions as typical for low-cycle fatigue problems. The crack opening stress and the cyclic crack-tip opening displacement are significantly influenced by the local grain structure. While the stabilized crack opening stresses obtained with the microstructure-based finite-element model are in good accordance with the von Mises plasticity results, the differences in the cyclic crack opening displacement are addressed to the asymmetric plastic strain fields in the plastic wake behind the crack-tip of the microstructure-based model. The asymmetric plastic strain fields result in discontinuous and premature contact of the crack flanks.

A methodology for assessing short fatigue crack growth in DCI materials affected by intergranular embrittlement at temperatures nearby 400 °C

A crack growth model for assessing the lifetime and short fatigue crack growth of ductile cast iron materials is proposed. The model bases on the assumption that the crack advance per cycle correlates with the cyclic crack tip opening displacement. Intergranular embrittlement at medium temperatures is accounted for as a temperature and strain rate dependent crack accelerating mechanism. The model is calibrated and successfully applied to predict temperature dependent fatigue lifetime and short crack growth of a ductile cast iron material.

Characterization of fatigue crack growth by cyclic material forces

The study at hand introduces a new approach to characterize fatigue crack growth at small strain elastoplasticity by cyclic material forces, cyclic configurational forces. In the theoretical framework, analyzing cyclic processes, the balance of cyclic energy momentum is derived using the cyclic free energy instead of the free energy. Moreover, the cyclic material forces acting on an inclusion within an elastic homogeneous body are derived using a modified version of Eshelby’s thought experiment. In the numerical context, cyclic nodal material forces are calculated using the weak form of the balance of cyclic energy momentum. Cyclic crack driving forces and cyclic global material forces are approximated using cyclic nodal material forces. The obtained cyclic global material forces are path-independent and show a linear correlation with the cyclic crack tip opening displacement. It is also able to characterize the effects of a single tensile overload. Finally, the results of the new approach are validated by comparing them to the experimental cyclic J-integral of a compact tension specimen.

Modelling of the fatigue crack growth of a coated single crystalline nickel-based superalloy under thermal mechanical loading

The focus of this paper is the simulation of fatigue crack growth of the coated single crystalline nickel-based superalloy PWA 1484 under thermal mechanical loading. Thus, two physical models are superimposed in terms to firstly calculate the deformation behavior under instationary thermal and mechanical loading (TMF) and secondly to model crack propagation after initial brittle cracking of the coating layer on the basis of cyclic crack-tip opening displacement (CTOD). All material parameters implemented in the models were evaluated from monotonic isothermal tensile and creep tests as well as from isothermal low cycle fatigue (LCF) experiments. The calculated fatigue crack growth was validated by in situ crack growth measurements using the beachmark technique. Hence, crack propagation initiated by the brittle coating system closely to the experimental results using rectangular flat specimen geometry instead of corner-crack (CC) specimens. The comparison of the simulated lifetimes to the experimental results provides remarkable accuracy of the physically-based lifetime model.

Quantitative in Situ SEM High Cycle Fatigue: The Critical Role of Oxygen on Nanoscale-Void-Controlled Nucleation and Propagation of Small Cracks in Ni Microbeams.

This Letter presents a quantitative in situ scanning electron microscope (SEM) nanoscale high and very high cycle fatigue (HCF/VHCF) investigation of Ni microbeams under bending, using a MEMS microresonator as an integrated testing machine. The novel technique highlights ultraslow fatigue crack growth (average values down to ∼10-14 m/cycle) that has heretofore not been reported and that indicates a discontinuous process; it also reveals strong environmental effects on fatigue lives that are 3 orders of magnitude longer in a vacuum than in air. This ultraslow fatigue regime does not follow the well documented fatigue mechanisms that rely on the common crack tip stress intensification, mediated by dislocation emission and associated with much larger crack growth rates. Instead, our study reveals fatigue nucleation and propagation mechanisms that mainly result from room temperature void formation based on vacancy condensation processes that are strongly affected by oxygen. This study therefore shows significant size effects governing the bending high/very high cycle fatigue behavior of metals at the micro- and nanoscales, whereby the stress concentration effect at the tip of a growing small fatigue crack is assumed to be greatly reduced by the effect of the bending-induced extreme stress gradients, which prevents any significant cyclic crack tip opening displacement. In this scenario, ultraslow processes relying on vacancy formation at the subsurface or in the vicinity of a crack tip and subsequent condensation into voids become the dominant fatigue mechanisms.

Towards a temperature dependent and probabilistic lifetime concept for nodular ductile cast iron materials undergoing isothermal and thermo-mechanical fatigue

In this investigation, the fatigue behaviour of a ductile cast iron with high content of silicon and molybdenum, was experimentally characterized by performing isothermal low cycle fatigue (LCF) tests as well as out-of-phase thermomechanical fatigue (OPTMF) tests within the temperature range RT – 500 °C. The studied material shows an embrittlement at temperatures nearby 400 °C. A possible explanation for the observed lifetime reduction is intergranular embrittlement (IE). A mechanism based lifetime model is proposed for assessing the lifetime. The model is based on the assumption that the crack advance per cycle is correlated with the cyclic crack tip opening displacement (ΔCTOD) attributed to the crack tip blunting caused by accumulation of plastic and creep deformations ahead of the crack tip. Intergranular embrittlement is accounted for by introducing a temperature and strain rate dependent prefactor in the crack growth law, which only acts in a certain temperature range. The model is calibrated for a GJS material and successfully applied to predict the lifetime of this material when undergoing isothermal and non-isothermal mechanical loadings. A probabilistic interpretation of the scatter of the investigated material is presented in conjunction with the random nature of the initial defect size distribution.

Experimental investigation of the time and temperature dependent growth of fatigue cracks in Inconel 718 and mechanism based lifetime prediction

The following contribution deals with the growth of cracks in low-cycle fatigue (LCF) and thermomechanical fatigue (TMF) tested specimens of Inconel 718 measured by using the replica method. The specimens are loaded with different strain rates. The material shows a significantly higher crack growth rate if the strain rate is decreased. Electron backscatter diffraction (EBSD) is adopted to identify the failure mechanism and the misorientation relationship of failed grain boundaries in secondary cracks. The analyzed cracks propagated mainly transgranular but also intergranular failure can be observed in some areas. It is found that grain boundaries with coincidence site lattice (CSL) boundary structure are generally less susceptible for intergranular failure than grain boundaries with random misorientation. For modeling the experimentally identified crack behavior an existing model for fatigue crack growth based on the mechanism of time dependent elastic–plastic crack tip blunting is enhanced to describe environmental effects based on the mechanism of oxygen diffusion at the crack tip. For the diffusion process the temperature dependent parabolic diffusion law is assumed. As a result, the time dependent cyclic crack tip opening displacement (ΔCTOD) is used as representative value to describe both mechanisms. Thus, most of the included model parameters characterize the deformation behavior of the material and can be determined by independent material tests. With the determined material properties, the proposed model describes the experimentally measured crack growth curves very well. The model is validated based on predictions of the number of cycles to failure of LCF as well as in-phase and out-of-phase TMF tests in the temperature range between room temperature and 650°C.

A crack tip driving force model for mode I crack propagation along linear strength gradient: comparison with the sharp strength gradient case

In the present work, based on the Dugdale criterion, a closed-form theoretical crack tip driving force model of simple expressions was proposed for static and fatigue crack propagation along a linear yield strength gradient (YSG). Qualitative and quantitative analyses of the YSG effect on the crack tip driving force are given. The crack tip driving force depends on the yield strength at the crack tip, the YSG within the plastic zone and the applied load. A positive (or negative) YSG has a shielding (or amplifying) effect on the crack tip driving force. A difference of material-toughening mechanisms between smooth and sharp strength gradient was revealed both theoretically and numerically. In the linear YSG case, when a fatigue crack propagates along the YSG at a constant applied cyclic crack tip stress intensity factor, the cyclic crack tip opening displacement decreases (or increases) when the crack propagates towards a higher (or lower)-strength region; however, the cyclic crack tip stress intensity factor increases, no matter when the crack propagates towards a higher- or lower-strength region. This abnormal phenomenon causes theoretical and experimental challenges for characterizing the smooth strength gradient effect on the crack tip driving force.

Mechanisms and modeling of low cycle fatigue crack propagation in a pressure vessel steel Q345

The fatigue process near crack is governed by highly concentrated strain and stress in the crack tip region. Based on the theory of elastic–plastic fracture mechanics, we explore the cyclic J-integral as breakthrough point, an analytical model is presented in this paper to determine the CTOD for cracked component subjected to cyclic axial in-plane loading. A simple fracture mechanism based model for fatigue crack growth assumes a linear correlation between the cyclic crack tip opening displacement (ΔCTOD) and the crack growth rate (da/dN). In order to validate the model and to calibrate the model parameters, the low cycle fatigue crack propagation experiment was carried out for CT specimen made of Q345 steel. The effects of stress ratio and crack closure on fatigue crack growth were investigated by elastic–plastic finite element stress–strain analysis of a cracked component. A good comparison has been found between predictions and experimental results, which shows that the crack opening displacement is able to characterize the crack tip state at large scale yielding constant amplitude fatigue crack growth.

Does the cyclic J-integral [formula omitted] describe the crack-tip opening displacement in the presence of crack closure?

In this paper, the correlation of the cyclic J-integral, ΔJ, and the cyclic crack-tip opening displacement, ΔCTOD, is studied in the presence of crack closure to assess the question if ΔJ describes the crack-tip opening displacement in this case. To this end, a method is developed to evaluate ΔJ numerically within finite-element calculations. The method is validated for an elastic–plastic material that exhibits Masing behavior. Different strain ranges and strain ratios are considered under fully plastic cyclic conditions including crack closure. It is shown that the cyclic J-integral is the parameter to determine the cyclic crack-tip opening displacement even in cases where crack closure is present.

Assessment of microstructural influences on fatigue crack growth by the strip-yield model

The strip-yield model is a common tool to calculate the cyclic crack tip opening displacement and the fatigue crack growth life of structures in case of isothermal fatigue loading. The incorporation of a temperature-dependent yield stress already enables its application in thermal fatigue analyses. A further extension of the strip-yield model is presented here together with simulation results: The rheological Masing model consisting of spring-slider elements connected in parallel is used to describe the material’s stress–strain curve. It results in different yield stresses belonging to the numerous sliding frictional elements. These different yield stresses are randomly arranged along the crack ligament line instead of the usually applied constant yield stress. They depend on temperature as the procedure should still be used at non-isothermal loading. Besides an improved modelling of the mechanical material behavior the consideration of microstructural aspects of fatigue crack growth becomes possible by influencing the values of the yield stresses near the crack initiation site.

Effect of Low Temperature on Fatigue Crack Formation and Microstructure-Scale Growth from Corrosion Damage in Al-Zn-Mg-Cu

The strong effect of cold temperature on the fatigue resistance of 7075-T651 is established. As temperature decreases from 296 K to 183 K (23 °C to −90 °C), the formation life for cracking about pit and EXCO corrosion perimeters increases, microstructure scale crack growth rates decrease in the range from 20 to 500 μm beyond the corrosion topography, and long crack growth rates similarly decline. Fatigue crack surface features correlate with reduced hydrogen embrittlement with decreasing temperature fed by localized H produced during precorrosion for pit and EXCO-proximate cracks, as well as by crack tip H produced by water vapor reaction during stressing for all crack sizes. The importance of the former H source increases with decreasing temperature for cracks sized below 200 μm. Decreasing temperature to 223 K (−50 °C) eliminates the contribution of environmental H through interaction of reduced water vapor pressure in equilibrium with ice and reduced H diffusion. The Knudsen flow model and exposure parameter, \( P_{{{\text{H}}_{2} {\text{O}}}}/f \), enables improved modeling of temperature dependent crack propagation, but does not fully describe low temperature fatigue behavior due to possible rate limitation by H diffusion. Further decreases in MSC da/dN to 183 K (−90 °C) are related to reduced mobility of the corrosion-precharged H which may associate with vacancies from dissolution. Crack formation, and growth rates correlate with either elastic stress intensity range or cyclic crack tip opening displacement, and are available to predict corrosion effects on airframe fatigue for the important low temperature regime.

Time and Temperature Dependent Cyclic Plasticity and Fatigue Crack Growth of the Nickel-Base Alloy617B – Experiments and Models

Isothermal low cycle fatigue and thermomechanical fatigue tests are performed on Alloy617B in the solution-annealed and stabilized condition at temperatures between room temperature and 900 °C. In addition, the replica technique is applied to study the growth of microcracks. The Chaboche model is found to describe the cyclic viscoplastic behavior of both heats, except the pronounced cyclic hardening in the low-temperature branches of the TMF tests. A lifetime model based on the cyclic crack-tip opening displacement and the cyclic J integral is used to describe the measured lifetimes and crack growth rates. However, the description is not fully consistent, since the data for room temperature and for temperatures above 400 °C fall into two separate scatter bands.

Thermomechanical fatigue of 1.4849 cast steel – experiments and life prediction using a fracture mechanics approach

AbstractIn this paper the thermomechanical fatigue properties of 1.4849 cast steel, which is used for exhaust manifolds and turbochargers, are investigated and a fracture mechanics based approach is used for fatigue life prediction. Isothermal low-cycle fatigue tests and thermomechanical fatigue tests are conducted in the temperature range from room temperature up to 1 000 °C. Fractographic investigations show that fracture occurs predominantly intergranularly at 600 °C, whereas mixed transgranular and intergranular crack growth is found otherwise. The methodology for fatigue life prediction is based on a time and temperature dependent cyclic plasticity model, which describes the transient stresses and strains, and on a law for time and temperature dependent microcrack growth. The crack growth law assumes that the increment in crack length in each cycle, da/dN, is correlated with the cyclic crack-tip opening displacement, δCTOD. An analytical fracture mechanics based estimate of δCTOD is used, which is derived for non-isothermal loadings. The fatigue lives of the low-cycle and the thermomechanical fatigue tests are predicted well with the model. Only predictions for the low-cycle fatigue tests at 600 °C, where integranular fracture is predominant, are non-conservative.

Simulation of fatigue crack growth under large scale yielding conditions

A simple mechanism based model for fatigue crack growth assumes a linear correlation between the cyclic crack-tip opening displacement (ΔCTOD) and the crack growth increment (da/dN). The objective of this work is to compare analytical estimates of ΔCTOD with results of numerical calculations under large scale yielding conditions and to verify the physical basis of the model by comparing the predicted and the measured evolution of the crack length in a 10%-chromium-steel. The material is described by a rate independent cyclic plasticity model with power-law hardening and Masing behavior. During the tension-going part of the cycle, nodes at the crack-tip are released such that the crack growth increment corresponds approximately to the crack-tip opening. The finite element analysis performed in ABAQUS is continued for so many cycles until a stabilized value of ΔCTOD is reached. The analytical model contains an interpolation formula for the J-integral, which is generalized to account for cyclic loading and crack closure. Both simulated and estimated ΔCTOD are reasonably consistent. The predicted crack length evolution is found to be in good agreement with the behavior of microcracks observed in a 10%-chromium steel.

A model for the formation of fatigue striations and its relationship with small fatigue crack growth in an aluminum alloy

The fatigue crack growth process involves damage accumulation and crack extension. The two sub-processes that lead to fatigue crack extension were quantified separately in a recent model for small fatigue crack growth applicable to engineering alloys. Here, we report the results of an experimental investigation to assess the assumptions of that model. The fatigue striation formation in an aluminum alloy is modeled, and it is verified that the number of cycles required for striation formation is related to the cyclic crack-tip opening displacement. The striation spacing is related to the value of the monotonic crack-tip displacement. It is concluded that extensive crack-tip geometry changes due to plasticity in the aluminum alloy causes a reduction in the slope of the fatigue crack propagation curves. The implications of these results on the fatigue crack propagation lifetime calculations are identified.

Mechanism-based thermomechanical fatigue life prediction of cast iron. Part I: Models

In the present paper, mechanism-based models are developed to describe the time and temperature dependent cyclic plasticity and damage of cast iron materials. The cyclic plasticity model is a combination of a viscoplastic model with kinematic hardening and a porous plasticity model to take the effect of graphite inclusions into account. Thus, the model can describe creep, relaxation and the Bauschinger-effect as well as the tension–compression asymmetry often observed for cast iron. The model for thermomechanical fatigue life prediction is based on a crack growth law, which assumes that the crack growth per cycle, da/ dN, is correlated with the cyclic crack-tip opening displacement, Δ CTOD . The effect of the graphite inclusions on crack growth is incorporated with a scalar factor into the crack growth law. Both models can describe the essential phenomena which are relevant for cast iron materials.