Determination of evenness of mechanical strength for graphite electrodes Ⅰ

According to the test data of the mechanical strength of graphite electrodes, the m value was calculated based on Weibull model theory, which was used to determine the evenness of mechanical strength of graphite electrode. In this paper, the computational method, process and requirements were given.

The uniformity of the mechanical strength of the graphite electrode is essentially a reflection of the uniformity of its internal structure. A good-quality graphite electrode product not only has high mechanical strength, but also has a uniform structure. To judge the uniformity of the graphite electrode product structure, the current main method is to see the internal structure by sawing the product longitudinally. This approach will not only cause waste, but also increase the production cost. At the same time, the result of the judgment cannot be quantified and can only make qualitative judgments. If the method of using hollow core drills at both ends of the electrode to test the flexural strength can also be used to determine the uniformity of the structure, it is a good treatment method. For the specified batch of products, drill more than ten to thirty samples. By testing the flexural strength of the sample, using the Weibull model for data processing, and making a quantitative determination of the uniformity of the mechanical strength of the product based on the Weibull modulus, it is actually equivalent to the quantitative determination of the uniformity of the product structure.

The failure type of graphite materials is brittle fracture. The physical failure model is based on Griffith's fracture theory, that is, tip crack propagation theory. Material failure is caused by structural defects and has the fracture characteristics of brittle ceramic materials. Regarding the cumulative strength failure probability of brittle materials, the Weibull model can be used to analyze the problem of the mechanical strength uniformity of graphite materials from the cumulative strength failure probability. Currently available graphite electrode products have three types of mechanical strength, namely compressive strength, flexural strength, and tensile strength. Among them, the compressive strength is not obvious for crack growth, while the flexural strength and tensile strength are obviously for crack growth, but considering that it takes more time to process samples to measure tensile strength, it is unlikely to mass-process standard tensile strength graphite samples, while the processing of flexural strength samples is easier (standard sample size: Φ10 mm×120 mm ; Φ20 mm×160 mm; Φ30 mm×180 mm), each batch of electrode products can get 10~30 flexural strength test results, so we can use Weibull model to discuss the uniformity of graphite electrode mechanical strength issues based on the flexural strength test data. Therefore, each test of flexural strength or tensile strength can be regarded as a strength failure experiment.

Weibull model:

In formula (1): F(t) is the cumulative strength failure probability; t is the observed strength value; t₀ is a constant, also called a scale parameter; m is a constant, also called a shape parameter or modulus.

In the formula, F(t) can find the corresponding median rank in the median rank table as F(t) according to the different number of original strength data n; t is the specific test result of flexural strength or tensile strength.

Differentiate formula (1) to obtain its probability density function:

It can be seen from the above formula that only the value of m is a parameter with substantial meaning in the Weibull model.

1 Judgement of mechanical strength uniformity

Take the test results of the flexural strength of graphite electrodes (abbreviated as observed values) as an example. The data are the flexural strength test results of Φ450 mm×1890 mm 6FG7 high-power graphite electrode type II products in 2015 and 2016. Analyze this data to determine which year the mechanical strength of the product is more uniform.

First, sort the data (observations), and then check the corresponding median rank in the median rank table according to the number of data n as the cumulative intensity damage probability (F(t)). The results are shown in Table 1.

In order to facilitate the calculation of the shape parameter m value, the Weibull model is deformed, that is,

Weibull model

perform deformation processing.

The specific deformation process is as follows:

It is obtained after deformation treatment

The Weibull modulus m is:

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