Number of AE events N as a function of time scaled by the sample lifetime. The inset shows the data on a log-log scale. Energy rates as a function of scaled time.
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Left panel: individual experiments. Right panel: average. Left panel: scatter plot of the sample lifetime and energy of the largest event. Right panel: scatter plot of lifetime vs total acoustic energy during the entire experiment. The inset shows the CDF of the data normalized case by case by t c. The color code measures the intensity of the transmitted light [ a , b ] or the local surface deformation activity from low blue to high yellow [ c — f ].
Alava, and Pasi Karppinen Phys. Applied 11 , — Published 6 February Abstract Finding out when cracks become unstable is at the heart of fracture mechanics. Research Areas.
Creep Fracture Material failure Self-organized systems Stochastic processes. Acoustic techniques Optical techniques. Issue Vol. Authorization Required. Log In. Figure 3 An example of four different models for the crack-growth dynamics together with a power-law bulk creep response and the resulting specimen response.
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Figure 4 The probability density function of event energies for 26 experiments. Figure 5 a AE events [ N t ] over the creep experiment. Figure 6 Number of AE events N as a function of time scaled by the sample lifetime. Figure 7 Energy rates as a function of scaled time. Figure 8 Left panel: scatter plot of the sample lifetime and energy of the largest event. Figure 10 a , b Speckle patterns at two different times 20 ms delay.
Figure 11 Average process zone length as a function of scaled time. Sign up to receive regular email alerts from Physical Review Applied. Journal: Phys. Also, dynamic strain aging causes a minimum variation of ductility with temperature, a plateau in strength as well as a peak in work hardening.
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Experimentally determined mechanical properties such as ultimate tensile strength, yield strength 0. Approximation curves related to the same properties are presented using solid or dashed lines. These approximation curves relating to the mentioned properties describe their experimentally obtained values with greater or lower accuracy. To determine the accuracy of approximation, the coefficient of determination R 2 is used as a measure of accordance between experimentally obtained results and polynomial approximation and serves as a statistic that gives information on the fit of a model [ 36 ].
Dependence of mechanical properties on temperature: X6CrNiTi steel. The structure operating under certain environmental conditions is to be subjected to certain loads. It is also necessary to choose a material whose properties will meet the structure service life requirements, i. Besides, very important aspects, e. In accordance with this, several uniaxial tensile tests regarding determination of ultimate tensile strength were performed.
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In the so called descriptive error bars, Figure 4 , an analysis of ultimate tensile strength is shown where range R and standard deviation SD are used. The standard deviation was calculated as given in Ref. To assess the short-time creep behavior of the considered material or to predict its creep resistance, several uniaxial short-time creep tests were carried out. Data defining creep tests as well as material creep responses are shown in Figure 5 , Figure 6 , Figure 7 and Figure 8.
In these investigations short-time creep behavior was considered since most materials can be subjected to such temperature conditions occurrence of high temperature due to error in cooling, hazard, fire, etc. Only some of the special materials are intended to be used in structures designed for long term operation at high temperatures. In long term creep processes, however, special equipment for creep process monitoring is to be used.
In these tests, stress levels are selected in accordance with the 0. To perform a creep test, appropriate but usually expensive equipment is indispensable. Although the creep test shows deformation behavior of the material realistically, sometimes it is possible, based on known data of the behavior from similar conditions, to predict the creep behavior for the prescribed conditions.
In the following part there are two rheological models and one analytical method formula proposed to be used in creep modeling. All of the proposed tools can be used for modeling the first and second creep stages. The Burgers model is represented in Refs. All of the mentioned Equations 3 — 5 can be used for three different types of modelling, namely, for:. The first type of modeling, Equation 6a , denotes the modeling of one exactly defined creep curve that is described by the defined creep temperature and the defined stress level at this temperature.
The last type of modeling, Equation 6c , is the most useful and applicable one. Namely, this modeling covers an entire range of stress levels and temperature levels for the considered time range. In Table 2 , data relating to creep modelling are presented, while creep modelling curves are presented in Figure 9. Experimental and modeled creep curves: steel X6CrNiTi Modeling was performed using Equation 5 by applying the principle 6c.
In general, all of the above mentioned models for simulating creep behavior are considered to be satisfactory.
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However, an analytical formula is proposed as the best model. When rheological models are considered, then the Burgers model seems to be more suitable for the creep processes where the dominated creep phase is the steady-state phase, while for creep process with dominated transient phase more expressed parabolic shape , the SLS model is considered to be more suitable. Also, it needs to be said that any of the used models are more suitable when only a particular curve is selected to be modeled.
Undoubtedly fracture toughness is one of the most important material properties used to design structure against fracture. Fracture toughness is a parameter that defines material resistance to crack extension [ 40 ], and it represents a critical value of the stress intensity factor SIF or K , designated as K Ic. Designation K Ic indicates that this is a minimum value of fracture toughness determined by using a specimen that meets the plane strain conditions and besides, is tensile loaded first mode.
Fracture toughness is stated to be a subject concerned with predicting failure mode, especially one containing crack-like defects [ 41 ]. In engineering practice, fracture toughness can be experimentally determined by a number of standard tests [ 42 ].
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However, experiments related to the measurement of fracture toughness are not intended for materials that behave plastically. On the other hand, to avoid problems such as complicated manufacturing of the specimen, differences between the crack in the real structure, and the manufactured crack on the specimen, other methods existing for fracture toughness assessment are used. One of these such methods is the determination of the Charpy impact energy.
Correlation between the Charpy impact energy and fracture toughness was reviewed in Refs.
In these investigations the Charpy test was used to assess the fracture toughness. The specimens were machined from the material rod longitudinal direction. The formula used to assess fracture toughness is based on the measured Charpy V-notch impact energy, i. However, although this formula can be applied independently of the temperature, the CVN impact energy is inserted in it in accordance with the obtained result at the considered temperature.
The geometry of the specimens used in these investigations is shown in Figure 10 a. Experimentally obtained results of the Charpy V-notch impact energy and the calculated values of fracture toughness are presented in Figure 10 b. Charpy V-notch specimen and impact energy determination. As engineering structures are frequently subjected to different loadings, it is surely of interest to investigate the resistance of the material to failure at the mentioned loadings. It is known that when a material is subjected to a repeated load cyclic load , fatigue failure may result in fracture of the considered engineering element at a stress level that is much lower than the fracture stress corresponding to a monotonic tensile load.
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