Method for determining the service life and designing a component made of a material

Abstract

The present invention relates to a method for designing a component made of a material, as well as a method for determining the service life of a component made of a material, based on the fatigue strength of the material, the creep behavior of the material and the crack threshold value of the material, wherein a time-dependent creep fatigue strength is determined based on the fatigue strength and the creep behavior, wherein the time-dependent creep fatigue strength indicates a temporal limit value for a critical fracture mechanical load and thereby the service life of the component made of the material is determined

Description

The present invention relates to a method for determining the service life of a component made of a material and to a method for designing a component made of a material.Durability evaluation of high cycle and creep stressed components is of great importance for the operation of components subjected to mechanical vibrations and / or high temperatures.Known approaches for determining the service life are, for example, the "Palmgren-Miner rule" and the "Robinson rule", wherein here in each case the individual damage components of the cycles and of the creep are accumulated without taking into account the loading sequence. However, this does not allow a reliable determination of the service life.In contrast, in the Kitagawa-Takahashi approach, a criterion for the crack progress behavior is formulated. In the following, the extension according to El-Haddad is used, which specifies a limit value for a critical defect size at a specific mechanical stress, see El-Haddad, et al. "Fatigue Crack Propagation of Short Cracks". Journal of Engineering Materials and Technology, Vol. 101 Issue 1, 1979.The EI HADDAD curve is determined as follows: ΔK th is a material-specific critical stress intensity threshold value, starting from which material fatigue is triggered by a mechanical stress. Y is a geometry factor which describes the influence of the crack geometry, as well as that of the embedding geometry, on the stress field in the vicinity of the crack tip. The variable (a+a 0) in this case indicates a defect size, wherein a 0 is interpreted as a material-specific defect size. The criterion of El Haddad states that a crack with the defect size a is critical, grows and leads to material failure if the associated voltage swing width Δσ th( a) is exceeded.However, the consideration of El Haddad is time-independent and not valid during prolonged operation in the high-temperature range. In load scenarios with a medium-voltage component, creep damage occurs, for example, which is manifested, inter alia, by an additional and ignored porosity development at grain boundaries. Since nucleation and pore growth by creep occurs primarily at grain boundaries, polycrystalline materials in particular are susceptible to this porosity development.As a result of the pore growth, the permissible stress swing width is reduced and passes into the critical region for crack growth.O. Jordan, T. Beck, "Short-Time Creep Deformation of the Coarse-Trained Nickel-Base Alloy 247 and Its Implications on the High-Cycle Fatigue Behavior." Proceedings of the ASME Turbo Expo 2022. Rotterdam, The Netherlands, 2022. ASME and T. Bouchenot et al., "Life Prediction Modeling of Combined High-Cycle Fatigue and Keep." ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition, Vol. 10B: Structures and Dynamics. London, England, 2020, ASME, show that a creep pre-damaged material achieves a lower load cycle count than non-pre-damaged material. A high density of creep-induced damage was thereby demonstrated by fractographic investigations as causative of the failure.The previous concepts evaluate the life of creep and highly cycle stressed materials with phenomenological models, but not the interaction of creep and fatigue at the physical level.DE 36 20 355 A1 relates to a method for determining the remaining useful life of turbine components, which are generally used at relatively high temperatures, taking into account creep strain.JP H08-5 533 A relates to a device for detecting a fracture of a fatigue test body for performing a material strength test such as a fatigue test and a creep fatigue test.Proceeding from the known prior art, it is an object of the present invention to provide a method for determining the service life of a component made of a material.The object is achieved by a method for determining the service life of a component made of a material having the features of claim 1. Advantageous refinements emerge from the dependent claims, the description and the figures.Accordingly, a method for determining the service life of a component made of a material is proposed, based on the fatigue strength of the material, the creep behavior of the material and the crack threshold value of the material. According to the invention, a time-dependent creep fatigue strength is determined based on the fatigue strength and the creep behavior, wherein the time-dependent creep fatigue strength specifies a time limit value for a critical fracture-mechanical load and the service life of the component made of the material is thereby determined.Fatigue strength describes the ability of a material to withstand repeated loads, e.g., mechanical stresses, without failure or fracture. Materials are often subject to alternating loads, whether in the form of cyclic loads or repeated load changes. These repeated stresses may lead to material fatigue over time, which may lead to cracking and ultimately failure of the material. Fatigue strength is therefore an important aspect in evaluating the load capacity of materials and constructions, especially in applications in which mechanical stress occurs over extended periods of time.The fatigue strength of a material can be determined by various experimental tests in which samples are tested under cyclic loads until fracture. From these tests, one can estimate the lifetime of the material under certain load conditions.Fatigue strength is often represented as a Wöhler curve or an S-N curve which demonstrates the relationship between applied stress and the number of recoverable load cycles until failure. For this purpose, samples are loaded with a cyclical load with a constant period time, wherein the stress amplitude σ a or the strain amplitude ε a and the R value (R or Rε) are predetermined. Voltage-controlled tests are preferably considered below. In such fatigue tests, the stress amplitude and the associated number of cycles achieved are plotted against one another, whereby a Wehler diagram (or else an S-N diagram) is obtained. If the sample of material reaches about 10 8 cycles without failure at a given mechanical stress, fatigue strength is believed.In particular, the existence of a fatigue strength can also depend on a crack formation and / or a crack size and / or a pore size of the material, i.e. on a so-called defect size, as explained in detail further below. In principle, a material with a large defect size tends to have a lower cyclic lifetime until failure.Creep is a long term deformation phenomenon in which materials undergo plastic deformation over time under constant stress and at elevated temperature without exceeding the stress limit. Because of creep, nucleation and growth of creep-induced defects occur. Generally, the varying defect size can be expressed by the creep as a=a(t).According to the invention, a time-dependent creep fatigue strength is determined based on the fatigue strength, the creep behavior and the crack growth threshold, wherein the time-dependent creep fatigue strength specifies a time limit value for a critical fracture-mechanical load and the service life of the component made of the material is thereby determined.The time-dependent creep fatigue resistance takes into account not only the initial defect size a, but also the defect size a(t) that varies over time due to the creep damage. In particular, the creep behavior of the material can be taken into account by substituting the initial defect size a by the time-dependent defect size a(t) (a→a(t)), so that the fatigue behavior is not determined on the basis of an initial and time-invariable defect size, but on the basis of the time-variable defect size as a result of the creep damage:In this case, a(t) is the creep-induced and time-dependent description of the defect size and a c is the defect size of cracks / defects which already exist. This makes it possible to predict from what time a component made of a material as a result of the creep damage exceeds the limit value for a break-mechanical load and, as a result, material fatigue occurs. The limit value for a break-mechanical load is reached if the material is no longer permanently stable due to the defect size which varies over time.The time until the defect size exceeds the critical limit value of the fracture-mechanical load is referred to here as the service life of the component made of the material.The fatigue strength can be determined from a Takahashi-Kitagawa graph.The Takahashi-Kitagawa diagram describes the relationship between the magnitude of mechanical stress applied to the material and the defect size. The Takahashi-Kitagawa diagram can be used in particular to characterize the fatigue behavior of metallic materials based on a defect size in the material.The El-Haddad curve describes the fatigue strength of the material as a function of the defect size, which falls as the defect size increases. The El Haddad curve is a development of the Kitagawa-Takahashi approach in which the transition from fatigue strength to falling section is better described. Whereas the material fails above the El Haddad curve as a result of critical crack growth, the region below the El Haddad curve is defined as durable.In particular, the El Haddad curve in the Kitagawa-Takahashi diagram is asymptotically based on the fatigue strength and on the falling straight line of the threshold value. Exceeding a defect size via the EI HADDAD curve or via the critical limit value accordingly leads to material fatigue. Accordingly, it can be read by the El Haddad curve from which defect size material fatigue occurs with a constant mechanical load or the material is no longer durable.Fatigue of the material is due to growing defects in the material which are caused by creep and cyclic stress. In addition, interaction and further growth occur as a result of the cyclical stress, which leads to failure of the material. However, in the case of a small creep pore size due to a low mechanical load or low temperature, this does not lead to crack propagation, while when a limit value is exceeded, crack propagation takes place starting from the creep pores and material fatigue occurs.The creep behavior can be determined in the case of a static load on the component by a change over time in the pore sizes of the component.The creep behavior of a material can be determined by creep tests. Creep is a deformation mechanism in which a material has plastic deformation over time under a constant load. This behavior is particularly relevant for materials used in high temperature environments, such as power plant or aircraft engine components.The basic idea of a creep rupture test is to subject the material to a constant mechanical load and to measure the time-dependent deformation. To examine the creep behavior, the load exerted on the material, the temperature which is below the melting temperature of the material, and the time profile of the strain in the measurement section of the sample are correspondingly recorded.The creep tests carried out make it possible to characterize the creep behavior of a material and to determine important properties such as the creep rate, the creep rupture and the creep rupture strength. These data are of critical importance to assess the reliability and life of materials under certain operating conditions and to ensure that they meet the requirements of the application.However, the creep behavior is very complicated to determine, since the experiments must be carried out over a long period of time.Creep patterns such as the creep pore model can be mapped to creep behavior, which can describe creep behavior for a large variation of stress conditions.The porosity development due to creep is theoretically described with the creep pore model. It describes nucleation, growth and ingrowth of creep-induced pores as a function of mechanical stress, duration of stress, temperature and material coefficients. Under high-temperature conditions, creep pores or cavities are formed and grown, for example, by the tearing open of grain boundaries at triple points as a result of high mechanical loads, which are also referred to as w-type pores. If, on the other hand, low mechanical loads are present, diffusion processes are the main mechanism for the growth of the pores, which arise mainly at grain boundaries with a perpendicular orientation to the load direction (r-type). Furthermore, the creep pores may also be increased in size by growing together multiple poresThe creep pore model can be used to determine, in particular, the growth behavior by grain boundary diffusion from the mean stress, the strain rate and the material parameter for the grain boundary diffusion.The growth modelling of the creep-induced pores and the prediction of the pore sizes and their distribution allows the interaction of creep and cyclic fatigue to be described at the physical level using the Kitagawa-Takahashi approach. In particular, the creep pore model may include not only the diffusive pore growth model but also the growth of pores and cavities at triple points.A polycrystalline material is composed of a plurality of grains. During the solidification process, numerous small solidified regions, so-called crystallization nuclei, are formed depending on the cooling rate. Since the crystal nuclei are formed independently of each other, they do not have any long range order among each other. Metals therefore do not consist of a crystal with a long range of orders, but of many individual crystalline regions or crystallites, see Roessler et al., "Mechanical Behaviour of Materials", Springer Vieweg, 2019 (6th edition). These crystallites, or also called grains, are separated from one another by grain boundaries. A grain boundary is a lattice defect and separates regions of the same crystal structure but with different orientation, see Gottstein, "Material Science and Material Technology", Springer Vieweg, 2014 (4th edition). Since grain boundaries are regions with low bond energies and many lattice defects, they often serve as diffusion pathways and critically affect the properties of the material.The object set out above is furthermore achieved by a method for laying out a component of a material having the features of claim 6. Advantageous refinements of the method are evident from the dependent claims and from the present description and the figures.Accordingly, a method for designing a component of a material is proposed, comprising the following steps: indicating a desired boundary condition and a desired service life of a component made of a material, simulating the mechanical and thermal loads of the component, determining the service life of the component made of the material, adapting the desired boundary condition and / or the desired service life of the component made of the material and / or of the material of the component. According to the invention, the service life of the component made of the material is determined by the method mentioned above.For example, in a first step, a component is defined to meet a certain operating time in the case of a certain mechanical load. For example, the blade of a gas turbine should be designed for a service life of 10 years during operation at a specific rotational speed and temperature. For example, the material of the gas turbine may be a polycrystalline nickel-based alloyFor example, in a second step, the operation of the component made of the material is simulated, for example with a finite element simulation. The simulation makes it possible to extract the operating temperature and the mechanical load of the component.For example, in a third step, the simulated operating temperature and stress can be used to predict the creep behavior with the creep pore model, while the fatigue strength can be predicted with the mechanical stress. By combining the creep pore model with the fatigue strength, a time-dependent creep fatigue strength can be determined which indicates a maximum operating time when the creep behavior exceeds the El Haddad curve.For example, in a fourth step, it can result from the fact that a specific boundary condition has to be changed in order to achieve a specific lifetime of the component of the material. For example, the turbine blade may be used in an aircraft engine only up to a specific rotational speed. For example, the use of a gas turbine blade is designed only up to a specific temperature. However, it is also possible that the desired service life has to be changed. For example, a change in the desired service life may consist in the maintenance of the gas turbine having to be carried out more frequently.The desired boundary condition can accordingly be the maximum mechanical load or an index which leads to a maximum load.Preferred further embodiments of the invention are explained in more detail by the following description of the figures. The following are shown: FIG. 1 shows a schematic sequence of the method for determining the service life of a component; FIG. 2 is an exemplary Takahashi-Kitagawa diagram of a material; FIG. 3 shows an exemplary creep behavior of a material; FIG. 4 shows a schematic determination of the service life of a material; FIG. 5 is another exemplary Takahashi-Kitagawa diagram of a material; and FIG. 6 shows a schematic sequence of the method for designing a component.Preferred exemplary embodiments are described below with reference to the figures. Identical, similar or identically acting elements are provided with identical reference symbols in the different figures, and a repeated description of these elements is partly omitted in order to avoid redundancies.FIG. 1 schematically shows the sequence of the method for determining the service life of a component of a material. The method S 1-S 4 is based on the fatigue strength of the material, the creep behavior of the material, and the crack threshold of the material. In a first step S 1, therefore, the fatigue strength of the material is determined, and in the second step S 2, the creep behavior of the material is determined. In a third step S 3, a time-dependent creep fatigue strength of the material is determined on the basis of the determined creep behavior and the fatigue strength. The time-dependent creep fatigue strength takes into account the increase in the defect size a(t), which in turn influences the fatigue strength of the material. In a fourth step, the life of the component of the material is derived from the time-dependent creep fatigue strength.The various steps S 1 to S 4 are explained in the following figures.FIG. 2 shows a schematic Kitagawa-Takahashi diagram for a specific material which is determined in step S 1. A mechanical oscillation stress is plotted on the y-axis. The defect size is plotted on the x-axis.The entered EI HADDAD curve E separates the diagram into two different regions. In the region above the EI HADDAD curve E, material fatigue occurs due to critical crack growth, which originate from a defect having a critical size. In the region below the EI haddad, on the other hand, fatigue strength is present.The El Haddad curve E is asymptotically related to the fatigue strength and to the falling straight line of the threshold value ΔKt h, which is given by material parameters.For example, a material having an initial defect size a init is durable at a certain voltage, while it leads to material failure at a larger defect size a f. From the classic Kitagawa-Takahashi diagram, it is not possible to read the time at which the critical defect size, which is given by the El Haddad curve E, is exceeded.FIG. 3 schematically shows the growth pattern of the size of pores during creep. The size of the pore on the y-axis is plotted against the stress time on the x-axis and is determined in step S 2. Depending on the constant mechanical stress, the temperature and the material, the defect size in the material grows with a continuous time.In FIG. 4, a graph for determining the time-dependent creep fatigue resistance is schematically shown. For this purpose, the temporal growth profile of the pore size from FIG. 3 is used in the fatigue strength determination graph from FIG. 2, step S 3. As a result, the defect size of the x-axis of the graph is transformed into a time scale. In particular, this allows a time t init to be assigned to the defect size a init and a time t f. to the defect size a f.From FIG. 4, the time scale can now also be read when the defect size has increased the defects in the material by the creep behavior to such an extent that the critical defect size is exceeded, step S 4. The difference between the time t init and the crossing of the EI HADDAD curve E is called the lifetime t 1. The service life of the component of the material is thus determined.FIG. 5 shows further time-dependent creep fatigue resistance curves for a material representing the effect of material scattering. While the temperature T 1= T 2 as well as the stress σ 1= σ 2( and therefore also the R ratio) is identical for both curves, the strain rate %0020̇ε varies due to the material scattering, ε̇ 1 > ε̇ 2. If a higher strain rate is present, the defects grow more quickly and failure occurs earlier in time. Similarly, the defects grow more slowly at lower strain rates and the material fails later. It should be noted here that both curves of the time-dependent creep fatigue strength graph are based on the same KT fatigue strength graph. The time scale deviating from one another is based here on the different creep damage due to the different stretching rate.FIG. 6 schematically shows the sequence of a method according to the invention for designing a component from the material. In a first step A 1, the desired boundary conditions for a component are established, such as, for example, the maximum mechanical load and the maximum operating temperature. In a step A 2, the desired service life is defined under the desired boundary conditions. In a third step A 3, the operation of the component and in particular the mechanical and thermal loads of the component are simulated, for example in a finite element simulation.The simulation data provides a maximum mechanical load at a particular operating temperature. With these data, a creep pore model can be created which adjusts the defect size that varies over time. From the defect size variable over time, the fatigue strength can be converted into a dynamic fatigue strength and, as described above, the living noise of the component made of the material can thereby be determined. Finally, in a step A5, it is judged whether the life corresponds to the desired life. If this is not the case, the desired boundary conditions can be adapted, for example, in order to make the operation of the component more gentle. Conversely, however, the component can also be enabled for operation under more difficult boundary conditions. In particular, the service life can also be adapted. For example, the component may be released for longer operation, or the maintenance interval of the component may be shortened. If the service life corresponds to the desired service life, the component is completely designed from the material.Where applicable, all individual features illustrated in the exemplary embodiments can be combined with one another and / or interchanged without departing from the scope of the invention.List of reference charactersS1, S2, S3, S4 steps of the method for determining the service life; and A1, A2, A3, A4, A5 steps of the method for designing a component.

Claims

Method for determining the service life of a component made of a material, based on the fatigue strength of the material, the creep behavior of the material and the crack threshold value of the material, characterized in that a time-dependent creep fatigue strength is determined based on the fatigue strength and the creep behavior, wherein the time-dependent creep fatigue strength specifies a time limit value for a critical fracture-mechanical load and the service life of the component made of the material is thereby determined.The method according to claim 1, characterized in that the fatigue strength is determined from a Takahashi-Kitagawa graph.Method according to one of the preceding claims, characterized in that the creep behavior in the case of a static load on the component is determined by a change over time in the pore sizes of the component.Method according to Claim 3, characterized in that a creep pore model is developed for the creep behavior, which model replaces the creep behavior.Method according to Claim 4, characterized in that the growth behavior by grain boundary diffusion is determined by the creep pore model from the mean stress, the stretching rate and the material parameter for the grain boundary diffusion.Method for designing a component of a material, comprising the steps of: - indicating a desired boundary condition and a desired service life of a component made of a material, - simulating the mechanical and thermal loads of the component, - determining the service life of the component made of the material, - adapting the desired boundary condition and / or the desired service life of the component made of the material and / or of the material of the component, characterized in that the service life of the component made of the material is determined according to the method according to one of Claims 1 to 5.Method according to claim 6, characterized in that the boundary condition is the maximum mechanical load.Method according to one of Claims 6 or 7, characterized in that the simulation is a finite element simulation.Method according to one of the preceding claims, characterized in that the component is a power station component or an aircraft component, in particular is a gas turbine.Method according to one of the preceding claims, characterized in that the material is a polycrystalline nickel-based alloy.

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