Creep strain rate .

Log-log plot of tensile creep strain rate against applied stress for alumina and an alumina-17vol%SiC nanocomposite tested in tension at 1200°C. 

In the initial stage, known as primary creep, the strain rate is relatively high, but slows with increasing strain. The strain rate eventually reaches a minimum and becomes near-constant. This is known as secondary or steady-state creep. This stage is the most understood. The characterized creep strain rate , typically refers to the rate in this secondary stage. The stress dependence of this rate depends on the creep mechanism. In tertiary creep, the strain-rate exponentially increases with strain [1-9]. 

Each phase in a composite will typically have different elastic and creep properties. However, assuming strong interfacial bonding as a limiting case, compatibility requires that the total strain, and the total strain rate, of each constituent be equal. The total strain rate of each constituent, eiitot, is given by the sum of the elastic strain rate, ki ei, and the creep strain rate, e,. To satisfy compatibility, this sum must equal the total creep rate of the composite eCjto, ... 

High crack tip stresses cause fast crack tip creep in the creep zone surrounding the crack tip. As r- 0, ec ee, i.e., the creep strain rates are much greater than the elastic strain rates, but this intense creep is constrained by the surrounding elastic material which causes crack tip stress relaxation. This field is of the HRR type, where as r— 0 (referred to as the RR-field for Riedel and Rice3,34... 

For n> 3, as the crack begins to grow the elastic and the creep strain rates are of the same order of magnitude near the crack tip, i.e., 0(ke) = 0(kc) as r— 0, and the asymptotic stress field has been the form (referred to as the //R-field after Hui and Riedel40)... 

Fig. 37a aad b. Schematic representatiaii of plastic flow for the 2-process model (a) yield stress vs. applied strain rate flk) creep strain rate Ep vs. applied stress... 

Fig. 11.7. Examination of the success of the hypothesis of linear stress dependence of the creep strain rate in the high-temperature regime (adapted from Nabarro and de Villiers (1995)).

A glass-bonded alumina consists of the alumina grains (grain size 10 xm) separated by a 0.1 pm layer of glass. Determine the creep strain rate that could be obtained if the grains were allowed to separate by linear... 

C1291-95 Test Method for Elevated Temperature Tensile Creep Strain, Creep Strain Rate, and Creep Time-to-Failure for... 

Transient or primary creep Following a spontaneous elastic strain the creep rate (also referred to as the creep strain rate) decreases with time from an initially high value. This stage of creep is often represented by an equation of the form... 

Viscoelastic creep manifests itself in the time-dependent deformation of a material. Experimental data obtained from a laboratory creep test under constant applied stress for a viscoelastic solid is shown in Fig. 12.1. Traditionally, a creep curve consists of three stages. In the first stage, also known as primary creep, the creep strain rate decreases with time until it reaches a constant value. The second stage, known as steady state creep, is defined as the region where the slope of the creep strain is a constant with respect to time. In the third and final stage, termed tertiary creep, the creep strain rate increases with time through progressive failure and terminates with the rupture of the specimen. 

E s % s nominal tensile creep strain rate daVdf according to ISO 899-1... 

Depending on the length measurement system used either traverse path or extensometer or a clip gauge additionally the normative (Eq. 4.44) or nominal (Eq. 4.45) creep strain rate de/dt can be determined to describe static long-term behaviour of plastics. 

FIGURE 10. A comparison of creep strain rate vs. applied stress at different temperatures for three fibers which are formed by a combination of alumina and silica. (Reprinted, from reference 22, with kind permission of Marcel Dekker Inc.). 

Minimum creep rate was reached in all tests. In air, creep strain rates were below 10 s at 1000 and 1100 °C, and ranged from 1.5 x 10 to 6.0 x 10 s at 1200 °C. The presence of steam has negligible effect on creep strain rates at 1000 °C. The presence of steam accelerates creep rates of N720/A by two orders of magnitude at 1100 °C. 

Although it is possible to introduce non-linear visco-elastic models, the second common approach is to utilize existing metals creep models. There are a number of models and all express the creep strain rate as a function of stress and other parameters. Popular forms are given below for primary and secondary creep, respectively. 

Bailey power law is used to determine creep strain and creep strain rate. The MFC Omega method can he used to calculate accumulated and future strain, total damage and damage rate, creep rate, and remaining life. In addition there are several industry standards that provide guidelines, criteria, and design data for materials in the creep range. These are AFI-530, AFI-579, and WRC-443. 

Figure 2. Log-log plot of steady state creep strain rate versus tensile stress for GS-44 at 1200°C,...

In Fig. 6.88, creep strain and the creep-strain rate are shown versus time-quite similar to Fig. 6.1a and b. Analogous to curves Fig. 6.1a and b, the creep curves in Fig. 6.88a exhibit a primary stage and a well-developed second-stage creep over... 

Fig. 6.106 Tensile minimum creep strain rate versus time to rupture at different stresses in argon at 1000, 1100, 1200 and 1300 °C [99]. With kind permission of Elsevier...

Creep describes time-dependent permanent deformation of materials resulting from constant structural stress. The creep of polymers can be divided into two main stages primary creep and steady-state creep. The creep strain rate decreases with time in the primary creep and is constant in the steady-state creep. Strain recovery occurs with the removal of external load after a creep time. Therefore, the total strain (e) consists of three separate parts el, e2, and e3. The el and e2 are the immediate elastic deformation and delayed elastic deformation, respectively. The e3 is the Newtonian flow. It was found that the el and e2 decreased with increasing clay contenf indicating lower creep recovery with the addition of C20A. The creep compHance J, the ratio of strain and applied load, can be expressed as... 

Cold rolling led also to an increase in the creep strain and secondary creep strain-rate. The creep activation energy was found to increase with increasing rolling reduction. Within the secondary creep stage, the creep process in polypropylene is mainly due to the a-relaxation process and most of the creep strain was recoverable. 

Plastic flow characteristics of polycrystalline a-Th containing 0.04 to 0.97 at% (600 ppm) N have been reported by McLachlan [6] and Peterson, McLachlan [11]. Tensile flow stresses at 1% strain, a, were measured at 4.2 to 800 K under conditions of constant flow rates, 5 x 10" to 10" s and creep strain rates of 10 and 10 s at constant stress. The N in solid solution increases the alloy strength and resistance to flow as measured by a, which can be resolved into two components as follows ... 

Fig. 15. Steady plateau creep strain rate e vs stress a for drawn LPE. A R50 = 10 ) 0 R50 y-...

Fig.17. Sherby-Dorn plots of creep strain rate vs creep strain for drawTi polypropylene at 30 C, at indicated stress levels.

Another model that proposes the incorporation of primary and tertiary creep strain rates is the A- 2 model. This model proposes that the primary creep strain rate be represented as an exponential decay function of increasing creep strain, and the tertiary creep strain rate be represented as an exponential growth function of increasing creep strain. However, this model is relatively new and has not been validated with independent experimental reliability data across the industry. 

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