PSI - Issue 52

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Thi Ngoc Diep Tran et al. / Procedia Structural Integrity 52 (2024) 366–375 Thi Ngoc Diep Tran/ Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 5. Tensile strength calculated using different mesh sizes.

4. Numerical modeling of different structure realizations The mechanical material behavior depends on the microstructure of the material. The properties of the composites can be significantly influenced by varying particle parameters such as particle size, particle geometry, and particle distribution. In order to study the effect of the particle parameters on crack initiation and crack growth, various models based on particle variations are discussed below. 4.1. Models with circular particles As seen in previous modeling, the particle microstructure is quite complex in reality, where it varies in size and shape. This section aims to replace the complex particle geometry with circles while keeping the surface area and aspect ratio to the original irregular microstructure. First, the irregular particle must be constructed by a fitted ellipse by calculating the geometric measurements of this particle region (Fig. 6a), e.g., major axis length , minor axis length , center ( , ) , and angle between the x-axis and the major axis. The equations to describe an ellipse with an orientation angle are defined as follows (Papula (2017)): ( )= + cos( )cos( ) − sin( )sin( ), ( )= + cos( )sin( ) − sin( )cos( ). Finally, it should be examined whether there is a statistical significance between generated ellipses and original particle shapes regarding the aspect ratio. For this purpose, the particle length and the major axis length of the ellipse are compared using the Chi-square goodness of fit test (Fahrmeir et al. (2016)) at significance level =0.05 . Fig. 6b shows the relative frequency of elliptical and irregular particles according to the particle’s length. The Chi-square test of goodness yield the p-value = 0.74 >0.05 , i.e., there is no statistical difference at the significance level of 5% between the lengths of elliptical and irregular particles. In our case means that despite the change in particles’ microstructure geometry, the aspect ratio is statistically retained. It is practical from the fitted ellipse to convert to a circle. The centre remains the same and the radius of the circle is calculated as = √ / , where is the surface area of the particle. The circular particle is automatically generated in ABAQUS using Python. The corresponding model is referred to origin model for approximation with circles.