Experimentelle Charakterisierung und zweidimensionale Simulation der mikrostrukturbestimmten Ermüdungsrissausbreitung in einer β‐Titanlegierung

In this project the initiation and propagation of short fatigue cracks in the metastable β‐titanium alloy TIMETAL®LCB is investigated. By means of an interferometric strain/displacement gauge system (ISDG) to measure the crack opening displacement (COD) and the electron back scattered diffraction technique (EBSD) to determine the orientation of individual grains the microstructural influence on short crack initiation and growth can be characterized. Finite element calculations show a high influence of the elastic anisotropy on the initiation sites of cracks. Crack propagation takes place transgranulary along slip planes as well as intergranulary along grain boundaries. The crack growth rate depends strongly on the active mechanism at the crack tip which in turn is influenced by crack length, the applied stress and the orientation of the grains involved. The value of the steady state crack closure stress changes from a positive value at low applied stresses (roughness induced) to a negative one at higher applied stresses (due to plastic deformations at the crack tip). The crack growth simulation is realised by a two‐dimensional boundary element technique, which contains the ideas of Navarro und de los Rios. The model includes the sequence of the applied stress amplitude as well as the experimental measured roughness induced crack closure.     

A study of the influence of grain boundaries on short crack growth during varying load using a dislocation technique

The propagation of short cracks in the neighbourhood of grain boundaries have been investigated using a technique were the crack is modelled by distributed dislocation dipoles and the plastic deformation is represented by discrete dislocations. Discrete dislocations are emitted from the crack tip as the crack grows. Dislocations can also nucleate at the grain boundaries. The influence on crack growth characteristics of the distance between the initial crack tip and the grain boundary has been studied. It was found that crack growth rate is strongly correlated to the dislocation pile-ups at the grain boundaries.     

Grain boundary influence on short fatigue crack growth rate

The influence from different grain boundary configurations on the crack growth rate of a microstructurally short edge crack, located within one grain and subjected to remote fatigue loading, is studied. The study is performed using a dislocation formulation, were the geometry is described by dislocation dipole elements in a boundary element approach and the plasticity by discrete dislocations, located along specific slip planes in the material. Plane strain and quasi-static conditions are assumed. The crack is assumed to grow in a single shear mechanism due to nucleation, glide and annihilation of discrete dislocations. Different grain boundary configurations in front of the growing crack are considered, including both high angle and low angle grain boundaries. It is shown that both grain boundary configuration and distance between the crack and a grain boundary has a pronounced influence on the crack growth rate.     

Modelling of small fatigue crack growth interacting with grain boundary

The slip band at the tip of a small fatigue crack interacting with grain boundaries is modelled for four cases: a slip band not reaching the grain boundary, a slip band blocked by the grain boundary, a slip band propagated into an adjacent grain, and a slip band propagated through one and then blocked by a second grain boundary. The theory for continuously distributed dislocations is used to calculate the crack-tip sliding or opening displacement and the microscopic stress intensity factor under tensile and shear loading. Assuming that the range of the tip displacement directly determines the propagation rate of both Stage I and II cracks, prediction of the propagation behavior of a small crack is made as a function of the distance between the crack tip and the grain boundary, and of the difficulty to propagate slip into adjacent grains, as well as a function of crack length and stress level. The directions for further development of modelling are discussed.     

A model for short crack propagation in polycrystalline materials

A model for microstructurally short crack propagation in a grain structure of a polycrystalline material is developed. The crack propagation model is based on a crystal plasticity model and a microstructurally short crack propagation model in the spirit of the model by Navarro and de los Rios [A model for short fatigue crack propagation with an interpretation of the short-long crack transition. Fatigue Fract Eng Mater Struct 1987;10:169-86]. Numerical examples, where the combined crystal plasticity and crack propagation model is implemented in a model of a microstructure representing a duplex stainless steel, concludes the paper. Results showing how the misorientation of the crack- and slip-directions between two adjacent austenitic grains influences the crack propagation rate, as the crack propagates across their common grain boundary, are given.     

Micromechanical modeling of grain boundary resistance to cleavage crack propagation in ferritic steels

In ferritic steels a propagating cleavage microcrack changes its propagation direction as it advances from grain to grain. This is due to differences in the orientation of the cleavage planes of two neighboring grains. In order to reach a cleavage plane in a new grain, a microcrack must first penetrate the grain boundary. Grain boundaries therefore act as natural barriers in cleavage fracture. The influence of a grain boundary and the associated misorientation in cleavage planes on crack arrest is here examined using a 3D finite element model with axisymmetric periodicity, representing two grains whose cleavage planes are tilted and twisted relative to each other. The temperature dependent mechanical properties of ferrite are modeled using a temperature dependent viscoplastic response. The development of the crack front as the microcrack penetrates through a grain boundary is here presented. The influence of the twist misorientation on the critical grain size, defined as the largest grain size that can arrest a rapidly propagating microcrack, is examined in a temperature range corresponding to the ductile to brittle transition (DBT) region. It is shown that when both tilt and twist misorientation are present, the influence of tilt and twist, respectively, on crack growth resistance can be decoupled.     

In situ observations of crack propagation and role of grain boundary microstructure in nickel embrittled by sulfur

In situ observations of crack propagation in sulfur-doped coarse-grained nickel were performed for the specimens with grain boundary microstructure pre-determined by SEM/EBSD analysis. The role of grain boundary microstructure was studied in the crack propagation in nickel embrittled by grain boundary segregation of sulfur. It was found that the main crack tends to predominantly propagate along random boundaries, and the crack propagation rate can be locally accelerated at the grain boundary network with a high connectivity of random boundaries. On the other hand, the cracks can propagated along fracture-resistant low-Σ coincidence site lattice (CSL) boundary only when the trace of the grain boundary is arranged being almost parallel to slip bands in the adjacent grains. The local crack propagation rate was found to become lower when a crack propagated along low-Σ CSL boundaries. Moreover, when the crack propagation is inhibited by low-Σ CSL boundaries, the branching of propagating crack occurs at partially cracked triple junctions. The crack propagation can locally slow down due to the occurrence of crack branching. The optimum grain boundary microstructure for the control of sulfur segregation-induced brittle fracture is discussed on the basis of new findings obtained from the in situ observations on crack propagation and fracture processes in polycrystalline nickel.     

Propagation behaviour of microstructural short fatigue cracks in the high-cycle fatigue regime

In the high-cycle fatigue regime, it is assumed that crack initiation mechanisms and short fatigue crack propagation processes govern fatigue life of a component. Moreover, it is now becoming accepted that the conventional fatigue limit does not imply complete reversibility of plastic strain and is connected to crack initiation. However, interaction of the crack tip with microstructural barriers, such as, e.g. grain boundaries or second phases, leads to a decrease and eventually to a stop in the crack propagation. In the present contribution, examples for propagating and non-propagating conditions of short fatigue cracks in the microstructure of a duplex steel are given, quantified by means of automated EBSD. To classify the results within the scope of predicting the service life for HCF- and VHCF-loading conditions, a numerical model based on the boundary element method has been developed, describing crack propagation by means of partially irreversible dislocation glide on crystallographic slip planes in a polycrystalline model microstructure (Voronoi cells). This concept is capable to account for the strong scattering in fatigue life for very small strain amplitudes and to contribute to the concept of tailored microstructures for improved cyclic-loading behaviour.     

Effect of grain boundary microstructure on fatigue crack propagation in austenitic stainless steel

The effect of grain boundary microstructure on fatigue crack propagation in austenitic stainless steel was investigated in order to control fatigue crack propagation. The fraction of low-Σ coincidence boundaries in specimens was controlled by thermomechanical processing. The specimen with the higher fraction of low-Σ boundaries (73%) showed the lower propagation rate of fatigue crack than the specimen with the lower fraction of low-Σ boundaries (53%). The ratio of intergranular fracture segments to the total crack length was lower for the specimen with the higher fraction of low-Σ boundaries. Moreover, the roles of grain boundaries in the fatigue crack propagation were investigated in connection with grain boundary microstructure, i.e., the character distribution and geometrical configuration of grain boundaries. It is evidenced that the approach to grain boundary engineering is applicable to controlling fatigue crack propagation in austenitic stainless steel.     

Automated simulation of fatigue crack propagation for two-dimensional linear elastic fracture mechanics problems by boundary element method

In this paper, automated simulation of multiple crack fatigue propagation for two-dimensional (2D) linear elastic fracture mechanics (LEFM) problems is developed by using boundary element method (BEM). The boundary element method is the displacement discontinuity method with crack-tip elements proposed by the author. Because of an intrinsic feature of the boundary element method, a general growth problem of multiple cracks can be solved in a single-region formulation. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not necessary. Local discretization on the incremental crack extension is performed easily. Further the new adding elements and the existing elements on the existing boundaries are employed to construct easily the total structural mesh representation. Here, the mixed-mode stress intensity factors are calculated by using the formulas based on the displacement fields around crack tip. The maximum circumferential stress theory is used to predict crack stability and direction of propagation at each step. The well-known Paris’ equation is extended to multiple crack case under mixed-mode loadings. Also, the user does not need to provide a desired crack length increment at the beginning of each simulation. The numerical examples are included to illustrate the validation of the numerical approach for fatigue growth simulation of multiple cracks for 2D LEFM problems.     

Influence of grain boundaries on short crack growth behaviour of IGSCC

Understanding short crack behaviour is essential for predicting the lifetime of light water reactor components. However, crack growth rates of short cracks are unsteady due to microstructural obstacles such as grain boundaries. On the other hand, the statistical behaviour of short cracks can be deduced from crack size distributions. Some papers have pointed out that the crack size distributions obtained by stress corrosion cracking tests showed a kink in the distribution line. This kink suggests that the short crack growth rate is slow compared with that of long cracks. And it can be thought that the slow growth rate is caused by the microstructural obstacles. This study investigated the influence of grain boundaries on the short crack growth behaviour of intergranular stress corrosion cracking. A crack growth simulation model, which considered the mechanical effects of the crack kink and bifurcation by grain boundaries, was developed. The crack depth distribution obtained by the simulation also exhibited a kink in the distribution line as seen in the experimental results. This suggests that grain boundaries play an important role in short crack growth behaviour.     

A MODEL FOR SHORT FATIGUE CRACK PROPAGATION WITH AN INTERPRETATION OF THE SHORT-LONG CRACK TRANSITION

The behaviour of short cracks approaching growth barriers (e.g. grain boundaries) is considered. The crack model of Bilby, Cottrell and Swinden is applied to simulate the blocking of the plastic zone at the grain boundary and to obtain the stress concentration ahead of the crack as it approaches the barrier. The idea of the Hall-Petch type relationship that the transmission of slip across grain boundaries needs the previous achievement of a critical stress has been used. By making the crack growth rate proportional to the plastic displacement at the root of the crack the deceleration behaviour of short cracks and the existence of non-propagating cracks may be explained. The fatigue limit is related to the stress below which a crack growing in a single grain is unable to promote slip in the neighbouring grain. The different behaviour in the so-called long crack period has been rationalized in terms of the plastic zone exceeding the grain size. For this case, and in the grain completely included within the plastic zone, the Hall-Petch analysis must be applied. Hence the maximum back-stress sustained by this grain cannot exceed the yield stress. After this point the Bilby et al. model is used with uy as a friction stress (i.e. the Dugdale model). Finally use is made of Fracture Mechanics to correlate the results in the long crack phase.     

Modelling of short crack propagation – Transition from stage I to stage II

The propagation behaviour of short cracks under cyclic loading is simulated using a mechanism-based model for two-dimensional crack propagation in stage I. Experimental investigations on a duplex steel have been performed to characterise the different barrier effects of grain and phase boundaries, so that the crack propagation can be simulated in a real microstructure. The model allows the activation of additional slip systems resulting in a crack propagation on multiple slip bands, which is the preliminary step to stage II crack growth. By use of virtual microstructures based on Voronoi diagrams, it is possible to simulate the overall fatigue-crack propagation process starting from a microstructurally short crack in a single grain until the crack has crossed several (10–20) grains with just one model.     

The microstructure as crack initiation point and barrier against fatigue damaging

From the emission of dislocations till short crack propagation fatigue is a local process determined by the microstructure. We present experiments based on electron channelling contrast imaging (ECCI) as refined application of the scanning electron microscope (SEM) and new focused ion beam (FIB) technique like FIB crack initiation and FIB tomography which give detailed information about crack initiation and the interaction of short fatigue cracks with precipitates and grain boundaries as microstructural barriers. As main result the characteristic fluctuation in the propagation rate of short fatigue cracks in front of grain boundaries that has so far defied calculation can now be calculated analytically from the BCS-model and Tanaka model by using three constants measured in a single crystal.     

原奥氏体晶粒尺寸对珠光体钢组织及韧性的影响

探索了奥氏体晶粒尺寸对珠光体等温转变组织特征以及对韧性性能的影响规律.研究表明,在相同等温转变温度下,珠光体片层间距无明显变化,随奥氏体晶粒尺寸的增加,先共析铁素体量减少而珠光体团尺寸增加.珠光体断裂韧性受控于裂纹前沿塑性影响区尺寸(1～2)δc,其中δc为临界裂纹张开位移,当原奥氏体晶粒大于(1～2)δc时,裂纹扩展阻力主要来自穿越珠光体片层α、θ相的颈缩、破断.当原奥氏体晶粒尺寸接近或小于(1～2)δc时,裂纹主要沿晶界、珠光体团界、α+θ片层界面扩展,通过扩展路径发生多次弯折消耗能量,随原奥氏体晶粒尺寸增加,准静态断裂韧度J变化幅度较小.而冲击韧性缺口前沿塑性影响区远大于原奥氏体晶粒,大角度晶界将促使裂纹的转折而提高扩展阻力,提高裂纹前沿塑性区大角度晶界密度有利于提高冲击功,冲击韧性A随晶粒尺寸的增加显著下降.     

On the stress wave induced curving of fast running cracks — a numerical study by a time-domain boundary element method

Summary Fast crack propagation in dynamically loaded plane structures is investigated. The major point of interest is the evolution of the crack trajectory under the influence of stress waves which are generated and repeatedly reflected at the specimen boundaries. Since these waves may lead to arbitrary mixed-mode and time-dependent loading of the crack tip, both the direction and speed of crack advance are determined from a fracture criterion.Starting point is a system of time-domain boundary integral equations which describes the initial boundary value problem of a linear elastic body containing an arbitrarily growing crack. The unknown displacements and/or tractions on the exterior boundary and the displacement jumps across the crack are computed numerically by a collocation method in conjunction with a time-stepping scheme. Crack growth is modelled by adding new boundary elements of constant length at the running crack tip.The method proves to be of sufficient accuracy when applied to problems treated with other numerical techniques. Moreover, the simulation of dynamic crack propagation under various geometry and loading conditions enables the reproduction and analysis of complex phenomena observed experimentally.     

全层状TiAl基合金断裂中晶界的双重作用

通过SEM原位拉抻技术和双晶体压缩实验研究了全片层TiAI基合金晶界断裂行为。研究表明,在全层状组织的断裂行为中,晶界具有双重作用。一方面,微裂纹首先萌发于晶界区,其扩展方式取决于晶界两侧片层的取向。另一方面,不同类型的晶界对裂纹扩展的阻力不同,因而对全层状TiAI基合金韧性的作用不同,纵向晶界有助于断裂韧性的提高,而横向晶界对合金韧性不利。     

Cohesive zone representation and junction partitioning for crystal plasticity analyses

A novel scheme is presented for incorporating finite thickness cohesive interfaces in virtual grain structures for crystal plasticity finite element (CPFE) analyses of intergranular crack initiation and propagation. A Voronoi tessellation model is used to define the virtual grain structure, with automatically generated nonzero thickness cohesive zones (CZs) representing the grain boundaries and multiple junctions. An efficient grain boundary offsetting algorithm is presented, and issues related to automatically partitioning multiple junctions are discussed. Two feasible junction partitioning schemes are presented, the second of which has the advantage of partitioning junctions using uniform quadrilateral elements and naturally defining their normal and tangential directions. For the second scheme, a rule‐based method is presented that carries out the preliminary meshing of CZ junctions, including data representation, edge event processing, and cut and trim operations. A virtual grain structure modelling system, VGRAIN, is introduced to implement the proposed CZ junction partitioning method and directly generate meshed virtual grain structures with CZ grain boundaries for CPFE studies. To demonstrate the proposed junction partitioning and CZ representation schemes, two finite strain CPFE simulations are presented for plane strain uniaxial tension and three‐point bending, demonstrating large‐scale crack initiation and propagation under shear and opening modes. Copyright © 2012 John Wiley & Sons, Ltd.     

A quantitative three-dimensional in situ study of a short fatigue crack in a magnesium alloy

A previous four-dimensional in situ study of a short crack in a magnesium alloy King et al. (2011), Elektron 21, used synchrotron X-ray computed micro-tomography to follow its three-dimensional development with progressive fatigue cycling through the microstructure, which had been mapped by diffraction contrast tomography to measure grain shapes and crystal orientations in three dimensions. In the present work, very high-resolution post-test examination of the same sample by Serial Block Face Scanning Electron Microscopy (SBFSEM) provided three-dimensional fractographs to investigate the influence of microstructural features on the measured crack propagation rates. Digital volume correlation, applied to the X-ray computed micro-tomography datasets, measured the three-dimensional crack opening displacements and hence the crack opening modes. The short fatigue crack in magnesium propagated with mixed mode opening. Basal plane fracture is a dominant mechanism; hence, boundaries that disrupt the continuity of the basal plane are proposed to influence the crack propagation rate.     

Statistics and probabilistic modeling of simulated intergranular cracks

Using Monte Carlo simulation, the statistical properties of intergranular crack trajectories in polycrystalline materials are estimated. The polycrystalline microstructures are two dimensional and are modeled by a Poisson–Voronoi tessellation for the grain geometry and a uniform orientation distribution function for the crystallographic orientation. A heuristic is introduced for determining the path of crack propagation when the crack tip arrives at a grain boundary triple junction. This heuristic applies a combination of two criteria for determining the direction of crack propagation, the maximum circumferential stress criterion, and a criterion in which the crack is assumed to propagate in the direction with the least material resistance. The resistance of grain boundaries is assumed to be related to the crystallographic misorientation at the grain boundary. The trajectories of microcracks can be treated as a random process, and simulation results indicate that the crack process exhibits linear variance growth, the rate of which is related to the importance attached to the circumferential stress and the material resistance in determining the direction of propagation. The rate of variance growth is shown to vary with the average grain diameter, so that microcracks in polycrystals with small grain size will exhibit less spatial uncertainty. The statistics and distributions of the increments of the crack process are also given. Through a small change made to the normalization applied to non-dimensionalize the statistics, the results are extended to polycrystals that have spatially varying grain size. Finally, a probabilistic model is proposed that is able to produce synthetic crack trajectories that replicate the important statistical properties of the simulated cracks. Such a model may prove useful in studies of the transition from micro to macrocracking.