Abaqus 6.11 Crack =LINK=

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You should define the normal to the crack plane only if the direction is the same at all points along the crack line. If the direction of the normal to the crack plane varies along the crack line, you cannot select a single normal that defines the crack extension direction at all points along the crack line.

To define the normal to the crack plane, you can select points from an Abaqus native part (such as a vertex, datum point, or midpoint), or you can select nodes from an orphan mesh part. Alternatively, you can enter the coordinates of the points in the prompt area. If you select a point from an Abaqus native part and subsequently modify the part, Abaqus/CAE regenerates the points and updates the normal accordingly. If you are working with an orphan mesh part, you must select nodes that represent the start and the end of the normal.

q vectors If you select q vectors, you can define the crack extension direction, , directly by selecting points from the model that represent the start and end of the vector. If you are working with an orphan mesh part, you must select nodes that represent the start and the end of the vector. Alternatively, you can enter the coordinates of the points in the prompt area.

This option is used to define cracking and postcracking properties for the brittle cracking material model. The *BRITTLE CRACKING option must be used in conjunction with the *BRITTLE SHEAR option and must immediately precede it. The *BRITTLE CRACKING option can be used in conjunction with the *BRITTLE FAILURE option to specify a brittle failure criterion.

In this example an edge crack in a three-point bend specimen is allowed to grow based on the crack opening displacement criterion. Crack propagation is first modeled by giving the crack length as a function of time. The data for the crack length are taken from Kunecke, Klingbeil, and Schicker (1993). The data for the crack propagation analysis using the COD criterion are taken from the first analysis. This example demonstrates how the COD criterion can be used in stable crack growth analysis.

Once a crack-tip node debonds, the traction at the tip is initially carried as a reaction force at that node. This force is ramped down to zero according to the amplitude curve specified under the *DEBOND option. The manner in which the forces at the debonded nodes are ramped down greatly influences the convergence of the solution. The convergence of the solution is also affected by reversals in plastic flow due to crack propagation. In such circumstances, very small time increments are required to continue the analysis. In the present analysis the *CONTROLS, PARAMETER=FIELD, FIELD=DISPLACEMENT option is used to relax the tolerances so that more rapid convergence is achieved. Because of the localized nature of the nonlinearity in this problem, the resulting loss of accuracy is not significant. The *CONTROLS option is generally not recommended.

In the case when the crack length is given as a function of time, the second step in the analysis consists of letting the crack grow according to a prescribed crack length versus time relationship, using the data taken from Kunecke, Klingbeil, and Schicker.

The loading of the specimen and the specification of the COD criterion for crack growth demonstrates the flexibility of the COD criterion on the *FRACTURE CRITERION option. Frequently, the crack opening displacement is measured at the mouth of the crack tip: this is called the crack mouth opening displacement (CMOD). The crack opening displacement can also be measured at the position where the initial crack tip was located. Alternatively, the crack-tip opening angle (CTOA), defined as the angle between the two surfaces at the tip of the crack, is measured. The crack-tip opening angle can be easily reinterpreted as the crack opening at a distance behind the crack tip. In this example the COD specification required to use both the CMOD and the CTOA criteria is demonstrated.

For the purposes of demonstration the crack opening displacement at the mouth of the crack is used as the initial debond criterion. The first three nodes along the crack propagation surface are allowed to debond when the crack opening displacement at the mouth of the crack reaches a critical value. To achieve this, the following loading sequence is adopted: in Step 1, the specimen is loaded to a particular value (*DEBOND is not used), and in Step 2 the first crack-tip node is allowed to debond (*DEBOND is used). Steps 3 and 4 and Steps 5 and 6 follow the same sequence as Steps 1 and 2 so that the two successive nodes can debond. Since, the crack opening displacement is measured at the mouth of the crack, the value of the DISTANCE parameter on the *FRACTURE CRITERION option is different in Steps 2, 4, and 6.

The loading sequence adopted above outlines a way in which the CMOD measurements can be simulated without encountering the situation in which the COD is measured beyond the bound of the specimen, which would lead to an error message. In this example, the loads at which the crack-tip nodes debonded were known a priori. In general, such information may not be available, and the restart capabilities in Abaqus can be used to determine the load at which the fracture criterion is satisfied.

The remaining bonded nodes along the crack propagation surface are allowed to debond based on averaged values of the crack-tip opening angles for different accumulated crack lengths. The data prescribed under the *FRACTURE CRITERION option in Step 7 are the crack opening displacement values that were computed from the crack-tip opening angles observed in the analysis that uses the prescribed crack length versus time criterion. These crack-tip opening angles are converted to critical crack opening displacements at a fixed distance of 0.04 mm behind the crack tip. Hence, the crack opening displacement is measured very close to the current crack tip.

In addition, you must do the following in the Mesh module:If the assembly or part is two-dimensional, you must model the crack front with a ring of triangles and assign quadrilateral elements to the remainder of the contour integral region.

If you modeled the crack front with a ring of second-order triangles or wedges, Abaqus moves the midside nodes to the specified position along the element edges that radiate out from the crack tip or crack line. (If you modeled the crack front with a ring of first-order triangles or wedges, Abaqus ignores the position that you specified for the midside nodes.)

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In an engineering component containing a crack, residual stresses interact with stresses generated by applied loading in a complex manner. Typically, numerical techniques are required to predict the likelihood of fracture, providing results that are particular to the set of conditions considered. The work we describe here represents an attempt to understand the general behaviour of the crack for a simple geometry, loading and residual stress distribution that provides insight into the results of more complex analyses.

In general, a residual stress distribution is characterised by the magnitude and location of the peak residual stress and the spatial extent of its distribution. As an example, consider the as-welded residual stresses generated by a butt-weld between two identical plates. The magnitude of the peak residual stresses depends on the welding parameters and the material properties, including the phase transformation behaviour. Assuming symmetry the in-plane location of the peak residual stress is the centreline of the weld. Finally, the spatial extent of the residual stress distribution depends on the geometry of the weld and the thickness of the plates. We now introduce a through-thickness crack into the plate, symmetric about the weld centreline and subject the plate to a uniaxial applied stress in the direction parallel to the weld centreline. When the crack length is large compared to the extent of the residual stress distribution, the residual stress can be neglected, and a fracture analysis based only on the magnitude of the applied stress. Conversely, when the crack length is small compared to the extent of the residual stress distribution, the fracture analysis must use the sum of the residual stress and applied stress. When the crack length is similar to the extent of the residual stress distribution the analysis is more difficult: the crack is subject to stresses that vary with position and may in general cause parts of the crack surface to be in contact.

The form of the stress \(\sigma _{yy} \) at \(y=0\) versus x is equivalent to that of \(\sigma _{\theta \theta } \) versus r shown in Fig. 1a and is identical to that used by Terada (1976). Other stress functions could be used to generate a residual stress field and would give different detailed results to those presented here. Our aim however is to explore the effect of a simple residual stress field on the behaviour of a crack, although our simple residual stress field includes all the general attributes of a residual stress field.

In this section the elastic behaviour of a crack in a residual stress field is studied when subjected to additional tensile or compressive uniaxial applied stress. The geometry of the crack is shown in Fig. 1b. Depending on the length of the crack, the level of applied stress and the magnitude of the residual stresses the crack may be closed, partially open or fully open. These different crack states are defined in Fig. 5. A crack behaviour map may be used to describe the behaviour of the crack, where one axis represents the length of the crack and the other the level of the applied stress. Different states of opening of the crack occupy different regions of the crack behaviour map. We first present the crack behaviour map for positive \(\sigma _{\mathrm {RS}} \), that is when the tangential residual stress is tensile at the centre. Throughout this paper we will refer to this case as tensile residual stress. We then describe the analysis that allows the boundaries between the regions of crack behaviour to be found. Finally, we present the crack behaviour map for negative \(\sigma _{\mathrm {RS}} \), referred to here as the case of compressive residual stress. 2b1af7f3a8