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Simulation of surface crack propagation characteristics based on MSC Marc

Abstract: Based on MSC Marc software, this paper realizes parametric and modular modeling and automatic analysis through programming; The modular finite element modeling technology and contact technology are used to simulate the semi elliptical surface crack (leading edge), and the modeling method of forming radial singular cells at the leading edge of the crack and the contact technology are used to impose boundary conditions to realize the simulation of the singular stress field at the leading edge of the crack and the far-field stress of the crack model. On this basis, the J-integral of the crack front is calculated by using the crack virtual propagation technology, and the K-factor distribution of the crack front is converted by using the linear elastic finite element theory. The discrete nodes of the crack front are extended orthogonally, and the continuous crack propagation simulation is realized by fitting the crack front. The simulation results are basically consistent with the experimental results, which shows that the method used in this paper has good practicability

key words: contact technology; Singular element; Crack front; Semi elliptical surface crack; MSC Marc

most of the research on cracks at home and abroad focuses on theoretical derivation and experiments [1], and can only guide the reliability design of engineering structures through theoretical or empirical formulas. Many researchers [] introduced various theoretical calculation methods and distribution characteristics of stress intensity factors of surface cracks to characterize crack propagation. With the rapid development of computer technology and finite element technology, it is possible to simulate cracks and their propagation, which creates conditions for the reliability study of structures with cracks []

The virtual crack propagation technique and the definition of J-integral energy are the theoretical basis for the finite element method to calculate the stress intensity factor distribution at the crack front; The finite element method is the prerequisite to realize the continuous crack growth. Starting from the calculation of the J-integral (energy release rate) distribution of the crack front, the stress intensity factor distribution of the crack front can be converted in the case of elasticity. In this paper, the non synchronous propagation of crack front is realized by software. The shape assumption of the crack leading edge curve is not given in advance, but the crack leading edge is discretized into a series of points, the distribution of the stress intensity factor of the crack leading edge is calculated, that is, the local (each discrete point) stress intensity factor, and each discrete point of the crack leading edge is orthogonally expanded separately, and the obtained series of discrete points representing the new crack leading edge are fitted to obtain the shape expression of the crack leading edge curve, Realize the asynchronous propagation of the crack front (the propagation speed of each part of the crack front is different). In this way, more accurate propagation characteristics and life of typical cracks can be obtained1 establishment of continuous crack growth model

in order to truly simulate the stress field at the crack tip, this paper uses MSC Marc to simulate cracks, apply loads and boundary conditions, and uses parametric and modular modeling technology to establish a continuous crack growth model. Figure 1 shows a body with semi elliptical surface cracks

Figure 1 parametric and modular modeling of a block containing semi elliptical surface cracks

1.1 cracks

in MSC Marc software, the quarter model containing semi elliptical surface cracks is divided into seven modules, each module is represented as: crack carrier TETS, and the crack body includes three sub modules: crack1 module, crack2 module, fill module, Z-direction symmetry plane cracksym, X-direction symmetry plane symmx, and load application plane moving. The positional relationship between them is shown in Figure 2. By embedding the crack body into the crack carrier, the crack body can be divided into specific mapping lattice separately, and the crack carrier can be divided into four sides

Fig. 2 positional relationship between various modules

1.2 definition of crack front and its nodes

defined by contact technology, cracksym in the z-direction symmetry plane is only plastic deformation of the crack - characterized by irreversibility, the mechanism is slip and twin ligament parts, and symmetrical boundary conditions are not applied to the free surface of the crack, that is, cracksym is only bonded with TETS and crack1 modules of the crack, There is no connection with crack2 and fill modules. On the curve at the junction of module crack1 and crack2, the nodes of the two modules coincide, but the nodes of crack1 belong to the cracked ligament and are glued with the symmetry plane cracksym; The node of crack2 belongs to the free surface of crack and has no connection with cracksym; Thus, a three-dimensional crack front is formed at the junction curve of module crack1 and module crack2. The discrete nodes of the corresponding crack front curve are used to solve the local J-integral

2 leading edge discrete orthogonal propagation and fitting of semi elliptical crack model

figure, figure, figure, figure gives a graphical representation of the fitting process of semi elliptical crack leading edge propagation. The diagram shows that the crack front is discretized uniformly according to the arc length, and discrete nodes are used to replace the crack front; The figure shows the discrete points of the new leading edge obtained by orthogonal expansion of the discrete nodes of the leading edge. The newly obtained points cannot be directly used to represent the crack leading edge. To obtain the mathematical description of the crack leading edge, data fitting is required; Figure shows the ellipse fitting new discrete nodes to obtain the ellipse leading edge parameters; The graph shows the newly fitted elliptical crack front uniformly dispersed according to the arc length; Repeat the operations shown in Figure 3-2, Figure 3-3 and figure 3-4 to achieve continuous crack growth

2.1 orthogonal propagation calculation crack front node coordinates

the number of discrete nodes at the crack front is between 20 and 30 nodes. In order to clearly illustrate the problem, the number of nodes at the crack front in the figure is taken as 5. Suppose that the long semi axis of the elliptical crack is a, parallel to the X axis, and the price is loose in the middle and late March, and the short semi axis is B, parallel to the Y axis; The coordinate origin and the center of the ellipse are o, as shown in Figure 4

Fig. 4 orthogonal propagation of crack front nodes

the coordinate sequence of discrete points of crack front series is recorded as (x1, Y1) (xi,yi)... (xn,yn)。 Make the tangent L1i of the ellipse at the point (Xi, Yi), then the derivative of the point (Xi, Yi) is the slope of the tangent L1i, recorded as k1i. Calculate the derivative of X on both sides of the elliptic equation, and obtain:

the slope of the straight line L2I passing through the point (Xi, Yi) and perpendicular to the tangent L1i is recorded as k2i=-1/k1i; At the point (Xi, Yi), the crack propagation is △ AI. It is necessary to solve the coordinates of the point on the straight line L2I with a distance of △ AI from the point (Xi, Yi). The method is as follows:

in the program, the judgment method of the effective point is: substitute (Xi1, Yi1), (XI2, yi2) into the elliptic equation. If it is greater than 1, the point is outside the ellipse, that is, the point (Xi1, Yi1); If it is less than 1, the point is in the ellipse, that is, the point (Xi1, yi2). The crack extends outward, and points (Xi1, Yi1) are effective points

2.2 fitting the crack front and its step size control

ellipse fitting is performed on the discrete points of the crack front series, and the variable substitution can convert the ellipse fitting into linear fitting:

A and B can be calculated by the linear fitting of the least square method, so the major and minor axes a and B of the ellipse can be solved

Figure 5 error analysis of ellipse fitting crack front

as shown in Figure 5, the center of the coordinate system is O, the center of the ellipse is also o (0,0), and the coordinate sequence of the node after orthogonal propagation of the crack front is marked as (x1, Y1) (xi,yi),... (xn, yn), the new node obtained through the orthogonal propagation of the crack makes a straight line with the origin of the ellipse, and the distance from the new node to the origin of the ellipse is

the distance from the intersection of the fitting ellipse to the origin of the ellipse Op. The coordinate of point P is the intersection of line and ellipse. Define the relative deviation of the nodes at the crack front:

the step size of crack propagation is determined by controlling the error expressed in equation (8) to be no more than 1%, while ensuring the accuracy of fitting the crack front

3 semi elliptical surface crack continuous propagation simulation test

3.1 simulation test parameters

ZG25 material is used as crack block in the simulation test, and its propagation rate is: da/dn =1.44 × 1010（△K）2.79； Threshold value △ kth=6.3246 MPa · m1/2. Take a quarter of the block containing semi elliptical surface cracks as the finite element model, with thickness t of 10mm, width b of 15mm and length L of 15mm, as shown in Figure 1; A is the crack depth (short semi axis), C is the crack length (long semi axis), and A0 and C0 are the initial values. The crack front is divided into 22 parts, that is, discrete into 23 nodes; Each node is set with 4 J-integral radii, and 4 J-integral values can be calculated correspondingly. Calculate the K-factor range according to the fluctuating load

load parameters of simulation test are shown in Table 1. The load conditions are tension, bending and tension bending. The size of the load is determined so that there are four discrete points at the crack front, and the local K factor is greater than the threshold value. Using the same initial semi elliptical surface crack model: A0 = 2mm, a0/c0= 0.8; The equal step crack growth simulation is carried out. Table 1 load parameters of simulation test

3.2 simulation test results

simulation test results are shown in Figure 6

it can be seen from the change law of crack front in the figure, figure and figure that when the crack extends the same length (long axis C direction), the crack expands faster along the depth direction (short axis a direction) under tensile load, while it is slower under bending load, which is between the two under tensile and bending load; When the crack depth exceeds a certain size, the crack propagation along the depth direction gradually slows down and accelerates along the length direction under the three load conditions

The a/t-a/c relationship in the figure ofalso reflects that under tensile load, the crack expands faster along the depth direction, under bending load, the crack expands faster along the length direction, and under tensile bending load, it is between the two

3.3 comparison between simulation results and experimental results of samples

in this paper, the crack propagation experiment under tensile load is carried out, and the unknown results of simulation are compared with the experimental results, and the results shown in Figure 7 are obtained. Literature [12] is an experiment on four point bending specimens containing initial semi elliptical surface cracks with different a0/c0, in which the crack propagation until fracture is carried out. The shape of the crack front is monitored by the AC potential method, and the beach like stripes are left on the specimen section by the load reduction hook method. It can be seen from Figure 7 that the simulation results of the semi elliptical surface crack continuous growth model in this paper are basically consistent with the test results, which reflects that the semi elliptical surface crack continuous growth model in this paper is effective and feasible

Fig. 7 Comparison between the simulation results in this paper and the experimental results in literature [12]

4 Conclusion

this paper establishes a 3D crack continuous propagation model, and obtains the crack front edge of asynchronous propagation by compiling the interface program. The overall framework of the continuous crack growth model is realized. The semi ellipse continuous expansion simulation and experimental verification are carried out. The conclusions are as follows:

1 The evolution track of the crack front is semi elliptic, which shows that it is reasonable to use semi elliptic curve to fit the crack front in this paper

2. After the crack propagation depth exceeds a certain size, the crack propagation in the depth direction gradually slows down, and the propagation in the width direction accelerates, which is consistent with the semi elliptical crack propagation simulation results in this paper

3. Under load, the simulation results of the semi elliptical surface crack continuous growth model in this paper are basically consistent with the experimental results of crack growth characteristics, which shows that the semi elliptical surface crack continuous growth model established in this paper is effective and feasible

references

[1] Gao Qing, engineering fracture mechanics [m]. Chongqing: Chongqing University Press, l986

[2], Lin Xiao bin The Calculation of Stress Intensity Factor using 3D Finite Element Method[J]. CHINA MECHANICAL ENGINEERING. 1998, 9(11),

[3] Newman Jr J C, Raju I S. An empirical stress intensity factor equation for the surface crack[J]. Engng Fracture Mech, 1981, 15; 92

[4] Chen Daoli Fitting estimation of stress intensity factor of surface crack based on finite element analysis [j] Mechanical design and manufacturing, 2003,3, the measured force value is also different. 1

[5] Zhong Ming, Zhang Yongyuan Using time domain boundary element method

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