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Creo Elements Direct Drafting Crack
The micro-crack prorogation trend can be represented by the number and element death locations during the iteration analysis process (Figure 6 and Figure 7). Table 3 presents the dead element number at the initial, first, five, ten, and 20 iterations. The initial crack occurred around the S4 fixation screw (IT_1) and 46 elements were dead. After performing five iterations (IT_5), the number of dead elements rose to 121 and the micro-cracks around the S4 screw expanded. The element around the S4 screw continued to deteriorate and 160 elements at the upper circumference of the screw began to deteriorate after ten iterations (IT_10). Most of the bone around the S4 screw was damaged and the upper circumference of the S6 screw also had cracks that continued to twenty iterations (IT_20) (Figure 6 and Figure 7). However, there was no damage around the S1, S2, and S3 fixation screws.
Due to the complex process of the insulation layer patch in solid rocket motor (SRM), only manual patch could be used. Sometimes weak bonding or debonding in each joint surface was inevitable. This study is aimed at determining the crack group effect of insulation and interfacial debonded crack in the wide-temperature SRM. The crack group appeared in the front area of the ahead stress-release boot and was induced by low temperature, axial overload, or interface bonding failure. Based on the viscoelastic finite element method, singular crack elements and singular interfacial crack elements at the tips of crack group were established to calculate -integral. Varying according to the length and position of cracks, the -integral of crack tips was, respectively, calculated to prejudge their stability and the crack group effect. The results showed that collinear crack group appeared in the front stress-release boot layer, and the crack group had a certain shielding effect on the main crack when the SRM was launched at low temperature. When noncollinear crack group appeared in the front stress-release boot layer, the crack group effect changed with the length of the main crack. The crack group first had a shielding effect on the main crack and then had a strong strengthening effect. The experimental test of the simulated specimen revealed that numerical simulation results matched the experimental test results.
Typically, researchers use special elements to describe the particularity of the crack tip region [13, 14]. According to Equations (1) and (2), the first derivative of displacement at the crack tip obtains the stress , whose first derivative has singularity. To approximate displacement and stress at the crack tip to the real field, it is necessary to construct a singular element with displacement behavior so that the stress of the first derivative has singularity behavior.
The division of three-dimensional interface crack finite elements and the construction method of the -integral cylinder enclosure are shown in Figure 2. The interface singular crack element is used to describe the interface crack tip whereas other parts without cracks are described by ordinary elements. The solution of the three-dimensional -integral value of each crack and interface crack is mainly divided into two steps [15]: one is to calculate the two-dimensional -integral of the end crack as shown in Figure 2(a) and the plane () is perpendicular to the line in front of the crack (the intersection is node ).
The second step is to integrate the two-dimensional -integral point by point along the front line of the crack to obtain the three-dimensional -integral. In the structural finite element division, a closed cylindrical enclosure is constructed to surround the singular crack elements along the front line of the crack, as shown in Figure 2(a). The and are the outer surfaces and inner surfaces of the cylindrical enclosure, respectively. On the other hand, and are divided into two end faces of the cylindrical enclosure surface whereas is the two crack surfaces of the cracked body. For the interface crack, integrate the two-dimensional -integral point by point along the front line of the interface crack to obtain the three-dimensional -integral along the front line of the interface crack as shown in Figure 2(b). A closed cylindrical enclosure surface is formed to surround the front line of the interface crack. The two end surfaces of the cylindrical enclosure surface are and , the outer surface , the inner surface , and the upper and lower interface crack surface .
The surfaces , , , , and S5 together form the volume domain V. The surface integral can be transformed into volume integral by Gauss theorem [4, 10]. is the strain energy, and is the normal direction outside the surface. The unit vector of interface crack propagation direction was whereas is the volume weight function, the modulus of on the outer surface is 0, on the inner surface , and changes smoothly between two values in the surface. is the surface tension on end faces , , and interface crack surface . The -integral of each node along the line before the interface crack can be expressed as follows:
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We explore the entire form of S-Matrix elements of a potential C n-1 Ramond-Ramond (RR) form field, a tachyon and two transverse scalar fields on both world volume and transverse directions of type IIB and IIA superstring theories. Apart from 2ff7e9595c
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