CAE Fidesys 9.0 Documentation

J-integral 2D

Note: Use a triangular mesh to model the crack for best results.

Crack Parameter

The crack needs to be modeled in the preprocessor. To do this, we create a sideset for all crack nodes. There can be multiple such sidesets.

Crack tip

Modeled automatically at the junction of the crack curve and the rest of the model.

Contours

The default number of contours is 5, but the user can enter any value.

Under monotonic loading of elastic-plastic materials in modes I and II, the value of the J-integral does not depend on the trajectory, so the rate of energy release is determined by the contour very close to the crack tip.

Figure 1. Contour integral

Symmetrical Model

When solving a problem by cutting it into several parts, it is necessary to indicate its symmetry. Otherwise, the user receives an error.

Figure 2. Error

Figure 3. Quarter Model

Figure 4. Full Model

Plane Strain

Although the user already specifies the deformation type in the preprocessor, it must also be specified in the filter.

Plane Strain

Characterized by the fact that displacement of the body points and the crack tip occurs only in the x- and y-axis directions; in the z-axis direction, it is hindered. Deformation occurs only in one plane (e.g., xy).

Characteristics:

• At the crack tip, stress components act in all three directions;
• The stress state in the vicinity of the crack tip is three-dimensional (volumetric).

Plane-stress state

Characterized by the fact that in a solid, in a section with a crack, only the σx, σy, and τxy stress components act, while the σz, σxz, and σyz stress components are zero. All stress components act in a single plane (e.g., xy).

Characteristics:

• The displacement of points of a solid body in the crack tip region occurs in all three directions;
• The strain state in the vicinity of the crack tip is volumetric.

Example: stress state of a thin plate loaded with forces applied at its boundary parallel to the plate's plane and uniformly distributed across its thickness.

Advanced settings:

Minimum radius

Minimum radius of the integration region. Approximately half the size of the smallest element at the crack tip.

Figure 5. Length of the element at the crack tip

Flat radius

Radius of constancy of the weight function. Not less than twice the size of the smallest element at the crack tip.

Maximum radius

Sets the maximum radius of the integration region. Typically, no more than half the crack length.

Young's Modulus

Displays the value of this material parameter specified in the preprocessor. Unchangeable value.

Poisson Ratio

Displays the value of this material parameter specified in the preprocessor. Non-changeable.

Thermal Expansion Coefficient  

Displays the value of this material parameter specified in the preprocessor. Non-changeable.

Crack Normal, Component X

X coordinate of the crack normal.

Crack normal, Y component

Y coordinate of the crack normal.