Weibull modulus/parameter

The Weibull modulus, which is the parameter often of most interest, is obtained experimentally by testing a batch of samples. We need a large number of specimens to get an accurate value of m. Usually a minimum of 30 samples is required, which will typically give m within 20%. Up to 100 samples is not uncommon, which will give m with a greater than 90% confidence. 

Table IV - Strength distribution parameters Weibull modulus, m, and characteristic strength, oo (95%...

The material parameters in the Weibull distribution are related to the fracture toughness of the material, and also to parameters from the size frequency density of the cracks. (Details of this are available in Ref. [62].) For example, as shown in the noteworthy report of JayatUaka et al. [67], the Weibull modulus depends only on the slope of the crack size frequency distribution m = 2(p—1). 

Creep measurements of PRD 49 (PpBA) fibers at 65 °C and 150 °C exhibit logarithmic creep, as is also observed for PpPTA and PpBAT fibers at room temperature, and the creep rate increases with temperature [190]. Wu et al. determined Weibull parameters of the strength and lifetime distributions of PpPTA fibers at room and elevated temperatures [207]. They found that the mean filament strength (and Weibull scale parameter) varies inversely with temperature, while the strength variability (and Weibull modulus) remains practically constant over... 

In this equation, ctu is the stress below which Pr = 0 (a is often taken as CTu = 0). ct. is a scale parameter and m is the Weibull modulus that characterizes the width of the distribution. The right hand side of equation (7a) should be dimensionless which means that does not have the dimension of a stress. One way to take this feature into account is to normalize the volume (e.g., to replace V by V/Vo where V. is a reference volume). Additionally, if one considers a lot of cylindrical fibers of length L with a constant diameter, V can be replaced by L (or in a similar manner by L/U where L is a reference length). Assuming Ou = 0, equation (7a) can be rewritten in a linear form and used to derive the value of m from tensile test data. 

The tensile strength of Si-C-0 fibers decreases after exposure to elevated temperatures. When Nicalon NL 200 fibers are exposed for 1 hour to 1300 C in argon (P = 100 kPa), their mean tensile strength and scale parameter, Co, decrease by 45% while their Weibull modulus remains unchanged [80-83]. Fibers exposed to more severe conditions (e.g., for 5 hours in a vacuum at 1500°C) are so weak that they cannot be tested. Finally, the fact that oxygen-free fibers maintain their tensile strength under similar conditions relates to the absence of silicon oxycarbide and its decomposition process. 

Weibull modulus A parameter which characterizes the width of a monomodal Weibuli distribution. 

Lq = standard gage length m — Weibull modulus cr = tensile strength (To = a scaling parameter (T = an arbitrary parameter normally set to 0 F= cumulative probability of failure... 

Material Weibull modulus - m Volume scale parameter - sov (MPa.mm3/m)... 

Figure 13Sensitivity plot for the probability of failure of the TE device using 94 Monte Carlo simulations. The significant parameters influencing the Pf in order of importance are Weibull modulus of the TE material, scale parameter of the TE material, and elastic modulus of the TE material. 

Due to the lack of data, the volume-flaw characteristic strength and Weibull modulus at 1000°C were obtained by graphical interpolations of the corresponding values at RT and 1371°C as shown in Figure 9. Values obtained at 1000°C are listed in Table 1. In accordance with the aforementioned arguments, LS parameters were chosen for the analyses. 

---