Michael Marx

Calculating the Resistance of a Grain Boundary against Fatigue Crack Growth

One problem of the quantitative description of small fatigue crack propagation is the fluctuating crack growth rate induced by obstacles like grain or phase boundaries. Sometimes cracks stop completely for a large number of cycles sometimes cracks only decelerate, both resulting in an additional number of life time cycles. However, so far it is not clear, what actually determines the resistance of a grain boundary against fatigue cracks. Therefore we investigate small crack propagation through grain boundaries systematically by in-situ imaging in the scanning electron microscope and focused ion beam (FIB) crack initiation. By this unique technique, artificial stage I cracks with constant crack parameters can be observed while interacting with different grain boundaries which gives detailed information on the interaction mechanisms. We identified different useful aspects of the interaction between microcracks and microstructural barriers on the microscopic scale. 3D-tomographs revealed by serial sectioning and FIB give information about the transition process from the initial grain to the neighbouring one. The resulting purely geometrical consideration leads to a quantitative description of the blocking effect of grain boundaries and can be used to calculate the probability of a crack transfer from the orientation data of two neighboring grains only.

Microcracks in superalloys: From local in-situ measurements to lifetime prediction

Abstract The established K-concept with the Paris law as the central equation often used for life-time prediction and dimensioning does not fit with the micromechanical crack tip opening displacement (CTOD) concept. While the K-concept is based on continuum mechanics, the CTOD is influenced by the local microstructure. Consequently, the CTOD-concept is checked in situ in the scanning electron microscope and is found to be the appropriate micromechanical description of the crack propagation mechanism. However, it is shown that during low cycle fatigue of turbine materials, even under extreme conditions short cracks behave less harmfully than expected. Additionally a new technique of artificial crack initiation by operating with a focused ion beam is used to investigate special crack problems such as the interaction of cracks with microstructural barriers in detail, which was not previously possible in this systematic way.

Quantifying the grain boundary resistance against slip transfer by experimental combination of geometric and stress approach using stage-I-fatigue cracks

Abstract In recent studies, many groups have investigated the interaction of dislocations and grain boundaries by bi-crystals and micro-specimen experiments. Partially, these experiments were combined with supplementary simulations by discrete dislocation dynamics, but quantitative data for the grain boundary resistance against slip transfer is still missing. In this feasibility study with first results, we use stage-I-fatigue cracks as highly localised sources for dislocations with well-known Burgers vectors to study the interaction between dislocations in the plastic zone in front of the crack tip and selected grain boundaries. The stress concentration at the grain boundary is calculated with the dislocation-free zone model of fracture using the dislocation density distribution in the plastic zone from slip trace height profile measurements by atomic force microscopy. The grain boundary resistance values calculated from common geometric models are compared to the local stress distribution at the grain boundaries. Hence, it is possible to quantify the grain boundary resistance and to combine geometric and stress approach for grain boundary resistance against slip transfer to a self-contained concept. As a result, the prediction of the grain boundary resistance effect based on a critical stress concept is possible with knowledge of the geometric parameters of the grain boundary only, namely the orientations of both participating grains and the orientation of the grain boundary plane.

Stage-I fatigue crack studies in order to validate the dislocation-free zone model of fracture for bulk materials

Stage-I fatigue cracks are commonly described by the model of Bilby, Cottrell and Swinden (BCS model). However, since several experimental investigations have shown a dislocation-free zone (DFZ) in front of crack-tips, it is necessary to validate the new DFZ model and to examine the deviations to the BCS model. Therefore, the dislocation density distribution is derived from height profiles of slip lines in front of stage-I fatigue cracks in CMSX4® single crystals measured by contact-mode atomic force microscopy. This is possible, because the cracks are initiated at notches milled by focused ion beam technique directly on slip planes with a high Schmid factor. Consequently, the directions of the Burgers vectors are well known; it is possible to calculate the dislocation density distributions from the height profiles. The measured distributions are compared to the calculated distribution function of the DFZ model proposed by Chang et al. The additionally measured microscopic friction stress of the dislocations is then used to calculate the influence of grain boundaries on the dislocation density distribution in front of stage-I cracks. The calculation is done by the extended DFZ model of Shiue et al. and compared with the measured distribution function in polycrystalline specimens. Finally, the crack-tip sliding displacement as a measure for the crack propagation rate is compared for the DFZ model and the BCS model with the experimentally revealed values. The important result: the often used BCS model does not reflect the experimental measurements. On the contrary, the DFZ model reflects the measurements at stage-I cracks qualitatively and quantitatively.

Interaction of Cracks and Dislocations with Grain Boundaries Investigated by Focus Ion Beam Microscopy and Nanoindentation Technique

Abstract In this paper new techniques and combinations of common techniques are presented for creating well defined experiments to study the interaction of dislocations and cracks with interfaces under different loading conditions. So far, our knowledge results mostly from macroscopic tests like tensile tests or Wöhler tests. However, failure mechanisms operate on the microscopic level. When experiments are done on the same scale we obtain local information of the operating mechanisms instead of average data. The presented techniques are used to proof well known models as well as to investigate the physical mechanisms in detail. One of these techniques is nanoindentation which in our case is used to measure the interaction of dislocations with grain boundaries. Another technique is electron channelling contrast imaging combined with orientation gradient mapping for a further understanding of the development of self organized ordered dislocation structures. Finally artificial crack initiation and focused ion beam tomography are used to investigate the propagation of microstructural short cracks which can not be described by common fracture mechanics.

How to produce a desired bimodal microstructure for optimized mechanical properties: Investigation of the mechanisms of abnormal grain growth in pulsed electro-deposited nickel

Abstract Mechanical properties of metallic materials are often optimized by a specific heat treatment to adjust a required grain size. Thereby solute atoms, impurities or precipitates play an important role due to their retarding forces on the grain boundary movement. However, they not only stabilize small grain sizes during a heat treatment, it is also suggested that they introduce abnormal grain growth whereby for a small amount of grains the grain size increases tenfold and more. On the one hand abnormal grain growth impedes the adjustment of a required grain size; on the other hand it can be used to introduce bimodal grain structures which are known to combine opposing mechanical properties such as a high toughness and a high ductility. Therefore, the mechanisms of abnormal grain growth are investigated by varying the content of additives during the deposition process. Particle pinning is suggested as the mechanism responsible for abnormal grain growth at least in the initial stage, while a second phase may introduce extraordinary cubic grains growing abnormally in the late stage.

Influence of Grain Boundaries on Short Fatigue Crack Growth in “Polycrystalline CMSX-4”

Increasing the resistance of a material to fatigue crack growth by optimizing the microstructure is a major task of materials science. In this regard, grain boundaries and precipitates are well known to decelerate short cracks. Thereby the strength of the interaction is influenced by the crack parameters crack length and distance to the obstacles, the grain boundary parameters like orientation of the adjacent grains and the precipitate parameters like size and distance. A comprehensive understanding of the underlying physical principles is missing. The focused ion beam (FIB) microscope offers new possibilities for systematic experiments and three dimensional investigations to quantify the microstructural impact. The ion beam is used to cut micro-notches as initiation sites for cracks. Contrary to natural cracks the influencing parameters can be varied independently for a systematic investigation of the mechanisms. Additionally, the ion beam is used to make a 3D image of the crack path and the surrounding microstructural elements. The commonly single crystalline nickel base superalloy CMSX-4 served as a model material in a polycrystalline modification. Thereby it was possible for the first time to reveal quantitative data of the effect of microstructural barriers on short fatigue crack growth.

Thermal and Mechanical Stability of Nano-Crystalline and Nano-Structured Metals

The aim of the current work is to study the microstructure stability under thermal and mechanical loads of a nano-structured Cu/Co alloy and nc-Nickel with different content of solute elements and nano-particles. For this annealing at different temperatures as well as fatigue loading are performed and the microstructure evolution is characterized. The effectiveness of mechanisms that impedes grain growth (solute drag, Zener pinning) are evaluated and studied for both, thermal and mechanical loads.

How to Measure a Dislocation’s Breakthrough Stress to Estimate the Grain Boundary Resistance against Slip Transfer Based on the DFZ-Model of Fracture

Stage-I-fatigue-cracks are used as highly localized dislocation sources with well-known Burger’s vectors to study the interaction between dislocations and grain boundaries. This interaction in the plastic zone is of particular interest to understand the fluctuating crack growth in the very short crack regime. In the case of a blocked slip band the dislocations pile up at the grain boundary causing a local stress concentration. The resulting local stress distribution is calculated based on measurements of the dislocation density distribution in the plastic zone. For this purpose the slip line profiles were measured by AFM, the dislocation density distribution was determined and the dislocation-free zone model of fracture (DFZ) was validated. With this it is possible to quantify the grain boundary resistance and to combine geometric and stress approach for grain boundary resistance against slip transfer.

Using Barkhausen Noise and Digital Image Correlation to Investigate the Influence of Local Residual Stresses on Fatigue-Crack Propagation

Fatigue-crack propagation is, by far, the most crucial failure mechanism of technical systems. The key to understanding microscopic processes that lead to failure lies in the knowledge of local stresses, the driving force of cracks. We present the mapping of stress and strain fields induced by a single overload on a fatigue crack and their influence on transient crack-growth retardation. In contrast to former work, in which synchrotron x-ray diffraction (XRD) was used, this investigation was performed by using a calibrated magnetic Barkhausen noise microscope in combination with digital image correlation based on in situ scanning electron microscope imaging. The underlying mechanisms, residual stress effects in front of the crack tip and plasticity-induced crack closure caused by the plastic wake, have been studied. Specifically, a crack in S960Q steel has been followed through the overload (OL) region while examining measurements at distinctive overload points: before OL, after OL, at maximum retardation, and at recovery. We observe a strong correlation of the local fatigue-crack-growth rate with the local residual stress distribution obtained from magnetic Barkhausen noise, which remains nearly unchanged after the crack has passed by. Digital image correlation results reveal the influence of these residual stresses on crack-tip opening reactions and strain fields under external loads. Although strain fields show a strong decrease because of the OL event, differences in crack opening stresses remain rather low at first, but prevail in the second part of the OL region. The applicability of new measurement methods and their results regarding the dominating retardation mechanism are discussed. These indicate that the residual stress effect on the strain fields can be associated to be more significant than plasticity-induced crack closure at maximum retardation with a change of mechanisms on reacceleration.