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Analysis of the Opto-Mechanical Design Interface
Published in Paul Yoder, Daniel Vukobratovich, Opto-Mechanical Systems Design, 2017
A two-parameter Weibull distribution predicts probability of failure at a stress level σ based on testing of representative samples. The two parameters are the Weibull modulus m, which is dimensionless, and the scale factor, σ0, which is in units of stress. The Weibull modulus is the slope of the failure curve; it is also a measure of the variation in the sample data. Larger values of the Weibull modulus imply less variation. The scale factor is an indication of the mean strength of the sample; higher values imply increased strength. The two-parameter Weibull equation for the probability of failure Pf at some stress level σ is () Pf=1−exp[−(σσ0)m]
Ceramics and the Mechanical Properties of Ceramic Coating Materials
Published in Yichun Zhou, Li Yang, Yongli Huang, Micro- and MacroMechanical Properties of Materials, 2013
Yichun Zhou, Li Yang, Yongli Huang
The Weibull modulus is commonly used to characterize their strength uniformity. Factors such as manufacturing technology, porosity, inclusions, grain boundaries, grain structure, and uniformity have significant effects on the mechanical properties of ceramic materials. They are all the fatal weakness of ceramic materials. However, it is because of these chemical bonds that ceramic materials exhibit greater performance than metal materials in certain areas: (a) high hardness, which determines wear resistance; (b) high melting point, which determines outstanding heat resistance; and (c) high chemical stability, which determines excellent corrosion resistance. Although ceramic materials exhibit these special qualities, their fatal flaw-brittleness-limits their practical application. Therefore, the toughening of ceramic materials has become the core issue of ceramic material research worldwide [1,2].
Phenomenological Creep Models of Fibrous Composites (Probabilistic Approach)
Published in Leo Razdolsky, Phenomenological Creep Models of Composites and Nanomaterials, 2019
In materials science field, the shape parameter β of strength distribution is known as the Weibull modulus. The failure rate h (or hazard rate) is given by h(t;β,η)=βη(tη)β-1 $$ h(t;\beta ,\eta ) = \frac{\beta }{\eta }(\frac{t}{\eta })^{{\beta - 1}} $$
Mechanical properties of ZSM-5 extruded catalysts: calcination process optimization using response surface methodology
Published in Chemical Engineering Communications, 2021
For predicting the fracture load of a solid catalyst at a low probability of failure, the Weibull modulus is an index with a large influence, rather than the scale parameter (Wu et al. 2006). The larger the Weibull modulus, the steeper the Weibull distribution function and the narrower the mechanical strength data distribution, indicating that the fracture load is larger under a particular probability of failure. For example, the fracture loads of sample 3 are less than the loads of sample 16, but sample 3 has larger mean strength and Weibull parameter. The same is true for sample 11 and sample 1. In addition, the mean strength of sample 8 is the highest among all the samples, but since the Weibull modulus of sample 8 is smaller than that of sample 10, its fracture loads of the three low probabilities of failure are smaller than the fracture loads of sample 10. These analysis results indicate that it is desirable to use Weibull modulus as an approximation to evaluate the mechanical reliability of a solid catalyst particle, especially in the case where the mean strength of the comparative catalyst particles is very close.
Experimental and numerical investigation on size effect on crushing behaviors of single calcareous sand particles
Published in Marine Georesources & Geotechnology, 2021
Dumin Kuang, Zhilin Long, Ruiqi Guo, Piaoyi Yu
Figure 5 shows the relationships between the survival probability and single particle crushing strength according to Equations (12)–(16). It is demonstrated that for different particle sizes, the distribution of single particle crushing strengths follows a Weibull statistical distribution well. In addition, the characteristic crushing strengths of calcareous sand particles with different particle sizes of 5–7, 7–9, 9–11, 11–13, 13–15, and 15–17 mm are 4.72, 4.32, 3.40, 3.19, 2.47, and 2.18 MPa, respectively. It can be founded that the characteristic crushing strength decreases with the increase in particle size. Weibull modulus is determined by fitting the test data with Equation (16), as shown in Figure 5b. The corresponding Weibull modulus for six different particle sizes are 1.96, 1.96, 1.95, 1.90, 1.87, and 1.83 respectively. Generally, the Weibull modulus is a material constant independent of particle size (Huang et al. 2014). However, various researchers have reported that the Weibull modulus depends on particle sizes (Ma et al. 2019; Zhang et al. 2019). Jayatilaka and Trustrum (1977) stated that the Weibull modulus is related to the properties of the flaw size distribution of a material. In addition, as noted by Ma et al. (2019), the coral sand particles with larger sizes have more cracks and become more inhomogeneous in both mineral composition and geometric shape. Hence, the Weibull modulus seems to be slightly affected by the calcareous sand particle size.
Weibull distribution analysis of roselle and coconut-shell reinforced vinylester composites
Published in Australian Journal of Mechanical Engineering, 2021
S. Navaneethakrishnan, V. Sivabharathi, S. Ashokraj
where F is the probability of rupture of the material under uniaxial tensile stress , m is the shape parameter or Weibull modulus and σ0 is the scale parameter of the distribution. Weibull modulus, m, is related to the scatter of the data: the higher the m, the smaller the strength dispersion, and then the material is more uniform. It becomes the most important parameter of the distribution. The scale parameter is closely related to the mean strength.