Norton creep

The corresponding constitutive law for steady state contains elements named after Arrhenius (T-dependence) and Norton (a-dependence), both of them being strong functions of their parameters ds/dt = C o" exp(-QcyRT)-Even a small temperature difference would therefore produce an appreciable difference in the creep rate for a given applied stress, if the specimen was to be considered as a set of independent coaxial shells. This is equivalent to the... 

Creep behavior is such that even at constant stress and temperature, strain will develop as shown on the creep curve. According to the Norton-Bailey power law, which... 

There are several design methods utilized in the industry for analyzing creep problems. Three of the most prevalent are the Larson-MiUer relation, the Nor-ton-Bailey power law, and the MFC Omega method. The Larson-MiUer relation attempts to extrapolate creep rupture data from experimental results. The Norton-... 

There is no general empirical or mathematical equation to relate creep strain to metallurgy or temperature since it is a combination of all these factors. One common equation for creep strain is the Norton-Badey power law ... 

Fig. 6.19 Comparison of the minimum eieep rate data and the Norton power-law equation ( straight Unes) with stress exponent and activation energy equal to 12.6 and 1645 kJ/mol, respectively. Open and ftlled-in symbols represent the data above and below the experimentally observed transition region, respectively. Arrowed data imply the actual creep rate may be lower than the indicated one [35] with kind permission of John Wiley and Sons...

Remarks on Creep Rupture The Norton-Bailey Concept... 

Most creep analyses for long-term applications involve the determination of a steady-state or minimum creep rate and its examination as a function of applied stress and temperature. The steady-state or minimum, compressive creep rate (dc/ dtmin) may be related to the applied stress and temperature by an empirical Arrhenius power law or the familiar Norton-Badey creep equation . Often in creep testing, a minimal 1 % (of the expected lifetime) criterion is used. However, a 10 % criterion is preferable in order to obtain a meaningtid prediction of the usable lifetime for creep applications. In critical applications, such as for turbine components, an 25 % criterion is recommended, even preferred, so as to avoid failure by creep rupture. 

Norton s power law and an Arrhenius-type equation are the most common expressions describing the stress and temperature dependence of the steady-state creep rate. Of the many relations suggested to describe creep-rupmre life, the steady-state strain-rate relation was extended for the calculation of rupture strength and is used to predict service lifetimes. The Norton Bailey concept is used in regard to many solids, including ceramics (e.g., see Headrick et al. [50]). 

Norton FH (1929) The creep of steels at high temperatures. McGraw-Hill, New York... 

Also in this case, Y2O3 was added to the nanocomposite. The creep tests were performed by four-point bending at temperatures of 1200 and 1450 °C within a stress range of 50-150 MPa. The creep rate was calculated from the slope of the c versus t curve (Fig. 9.31) and steady-state creep was evaluated using Fq. (9.5), i.e., the Norton equation. An alternative explanation for the observed increase in creep resistance in the nanocomposite is that the SiC nanoparticles hinder the grain growth... 

Creep - The creep model used in CARES combines the classical Norton isothermal power law with a thermal process of constant activation energy showing the Arrhenius type of temperature dependence. Material creep data is determined by a log linear regression analysis of specimen steady state creep data determined at a variety of temperatures and stress levels. Similar to the oxidation analysis, data is examined by CARES to determine if it contains outliers. Any outliers are deleted prior to the final determination of the three material constants. 

At low temperatures (— 40 °C, or — 40 °F), it is even possible to induce a brittle fracture in a solder joint if steep temperature ramps are applied. The main fraction of creep deformation in Sn-Pb solder takes place in the tin phase. Given the absence of Pb-free specific data, it is necessary to use the data available for Sn-Pb solder for the design of tests for lead-free solder. If a Norton law is used to model the deformation behavior of solder (Eq 3), it is possible to evaluate how much DC and GBS are activated for a given strain rate at a certain temperature (Fig. 9). 

Norton creep 10 SnAg4.0Cu0.5 Cl, s-> 8 X 10-" Flip chip... 

Two common equations used for the steady state creep of solders are the Garofalo-Arrhenius and the Norton, given respectively as ... 

Flgnre 6.6 (a) Creep (time—strain) curves measured during two long-term tests at 600°C 90 MPa, 600°C, f pt = 94,000 h ( 10 years) and 70 MPa, 600°C, f p, 230,000 h (estimate, namely about 25 years) (steel grade 91) (b) stress—minimum strain rate curves and ass(x iated Norton law crrrves, at different temperatures (steel grade 91) [10]. 

There are two important special cases of Eqs. (26) and (30). For a solid which obeys Norton s creep law, i.e., creep rate is proportional to stress to the power n,... 

In case of compression tests, temperature and stress dependencies were determined according to the Norton power-law creep equation... 

Egff is the equivalent creep strain rate. In this case, a slightly varied Norton approach (equation 1) is chosen with a parameter A dependent on the creep strain and temperature so that... 

Table III lists the material properties of the components. Fibers and matrix were considered as isotropic, and in a first step the Norton-equation for steady state creep was assumed. Because of missing parameters for compression creep, tension creep data for the fibers were adapted from elsewhere The data for the matrix was estimated as follows. Based on the experimental results for the 0° and 90 fiber orientation the overall creep rate for the matrix was chosen higher and the stress exponent lower than for the fibers.

Table III. Material data for simulation - elastic and Norton-creep-constants, (equation 1).

Figure 10. Resulting strain rates of the unit cell simulations at a compression stress of 50 MPa at 1473 K. For both fiber and matrix a Norton creep law was used (parameters Table III).

Quite likely the sliding process is mainly responsible for the high creep rates of the 30 , 45 or 60° unit cells. Yet, a Norton aeep law was assigned to both fibers and matrix. Assuming that the matrix dominates creep in the 90 samples, its creep behavior can be better described by a primary creep law with regard to the experimental results (90 curve. Figure 4 left) ... 

A Norton creep law seems still appropriate for die fibers. After a short transient regime, experiments with fiber-dominated creep (0 curve Figure 4, left) owed an almost constant aeep rate. Therefore new simulations with different creep parameters for fiber and matrix (Table IV) were conducted. Figure 13 shows the resulting creep curves for the diosen parameters. 

Unit cells gave a qualitative impression of the interaction and stress redistribution between fibers and matrix in compression aeep. The effects of creep laws were investigated. As a result, fibers can be assigned to a Norton creep law whereas the matrix must be at least described with a primary creep law. For 0° and 90° samples the use of different creep laws for fiber and matrix was sufficient to capture the experimental results. However, the unit cell simulation resulted for the 45° sample In a higher defomiation than for the 90° sample, which is... 

The evolution of the strain rate during a tensile creep experiment under constant load usually exhibits three regimes a fast initial deformation, followed by a constant strain rate and a final increase of the strain rate before failure, referred to as primary, secondary and tertiary creep. Most of the data focuses on the second regime. For preliminary investigation, it can be recast in the form of the Norton law. Figure 4 depicts a comparison of experimental creep strain rate and predictions from calibrated Norton law, on the typical range of stress and temperature in an SOFC stack during operation. 

Where is the creq) strain rate(l/5), A and B are the creep constants of material, cr is the appUed stress, n is the stress exponent, Q is activation energy for creep deformation process,. R(=8.617DlO-5eF/A ) is Boltzmann s constant, and T is the absolute temperature. Moreovo-, the Norton power law creep equation can be also used to model the steady-state creep rate as a function of temperature and has the form in Equation (6). 

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