Crack mit

Crack propagation analysis can be performed for static or dynamic overloadings using the following procedures:. Implicit dynamic analysis using direct integration. Fully coupled thermal-stress analysis. It can also be performed for sub-critical cyclic fatigue loadings using the following procedure:. Low-cycle fatigue analysis using the direct cyclic approach.

When automatic incrementation is used for any criteria other than VCCT , enhanced VCCT , or low-cycle fatigue, you can specify the size of the time increment used just after debonding starts. By default, the time increment is equal to the last relative time specified. However, if a fracture criterion is met at the beginning of an increment, the size of the time increment used just after debonding starts will be set equal to the minimum time increment allowed in this step. The time increment size will be modified as required until debonding is complete.

The simulation of structures with unstable propagating cracks is challenging and difficult. Nonconvergent behavior may occur from time to time. While the usual stabilization techniques such as contact pair stabilization and static stabilization can be used to overcome some convergence difficulties, localized damping is included for VCCT or enhanced VCCT by using the viscous regularization technique. Viscous regularization damping causes the tangent stiffness matrix of the softening material to be positive for sufficiently small time increments.

For most crack propagation simulations using VCCT or the enhanced VCCT criterion, the deformation can be nearly linear up to the point of the onset of crack growth; past this point the analysis becomes very nonlinear. In this case a linear scaling method can be used to effectively reduce the solution time to reach the onset of crack growth. After the first crack-tip node releases, the linear scaling calculations are no longer valid and the time increment is set to the default value.

Cutback is then allowed. Therefore, the crack front is allowed to advance only a single node forward in any single increment although such an advance may take place across the entire crack front in three-dimensional problems. Because an analysis using the VCCT or enhanced VCCT criterion provides detailed results of the growth of the crack, you will need small time increments, especially if the mesh is highly refined.

Three different types of damping can be used to aid convergence for a model using the VCCT or enhanced VCCT criterion: contact stabilization, automatic or static stabilization, and viscous regularization.

Setting the value of the damping parameters is often an iterative procedure. If your VCCT model fails to converge due to unstable crack propagation, set the damping parameters to relatively high values and rerun the analysis. If the parameters are high enough, stable incrementation should return. However, the crack propagation behavior may have been modified by the damping forces and may not be physically correct.

To monitor the energy absorbed by viscous damping, plot the damping energy and compare the results to the total strain energy in the model ALLSE. When set properly, the value of the damping energy should be a small fraction of the total energy.

Monitor the damping energy to ensure that the results of the VCCT simulation are reasonable in the presence of damping. When you use contact or automatic stabilization, Abaqus writes the damping energy to the variable ALLSD in the output database. To maximize the accuracy of the debonding simulation, try to use matched meshes between the slave and master surfaces of the debonding contact pair. Printing contact constraint information to the data. By printing detailed contact conditions to the message.

For more information about these output requests, see About Output. The small clearance will help to eliminate unnecessary severe discontinuity iterations during incrementation as the crack begins to progress.

Do not use tie MPC s General multi-point constraints for the slave surface in a debonding contact pair. Abaqus is unable to resolve the overconstraint presented by the MPC and the debonded contact state. You may be able to help the analysis converge by adding geometric nonlinearity even if small-sliding is used for the debonding contact pair.

For more information, see Geometric nonlinearity. For two-dimensional models with contact pairs involving higher-order underlying elements, the initially unbonded portion must extend over complete element faces. In other words, the crack tip in a two-dimensional, higher-order model must start at a corner node on the quadratic slave surfaces. The crack tip must not start at a midside node. When the surface-to-surface contact formulation is used, at least two rows of elements should be used behind the crack front.

Dynamic effects are of utmost relevance when assessing the results from a debonding analysis using the VCCT criterion. In practical terms this requirement often translates into avoiding the use of mass scaling in the model. Use smooth amplitudes to drive the loading to help reduce the kinetic energy in the model.

Running the analysis over a longer period of time will not help in most cases because bond breakage is an inherently fast and localized process.

If appropriate, use damping-like behavior in the materials associated with the debonding plates to reduce dynamic vibrations.

If the vibrations are significant kinetic energy is clearly observable , the dynamic overshoot at nodes behind the crack tip may lead to premature debonding of the crack tip. To maximize the accuracy of the debonding simulation, use quad meshes between the slave and master surfaces of the debonding surfaces. Avoid using elements with aspect ratios greater than 2. In most cases mesh refinement will help with obtaining a realistic result.

Highly mismatched critical energy values between modes tend to induce crack propagation in continuously changing directions in a manner that may be unstable and unrealistic, particularly for modes II and III.

Do not use such values unless experimental data suggest so. Use frequent field output requests to evaluate the debonding evolution as the analysis progresses. In some cases this can point to nontrivial modeling deficiencies that are difficult to identify from a simple data check analysis.

Avoid the use of other constraints involving nodes on both surfaces of the debonding interface because the cohesive contact forces will compete with the constraint forces to achieve global equilibrium. Bond breakage might be hard to interpret in these cases. Table 2 describes the advantages and disadvantages of the two approaches. For an example of the use of cohesive elements, see Delamination analysis of laminated composites.

This example also shows the effect of viscous regularization on the predicted force-displacement response. You must obtain the critical strain energy release properties of the bonded surfaces for VCCT.

The procedure to obtain the critical strain energy release properties is beyond the scope of this guide; however, you can refer to the following ASTM test specifications for guidance:. Initial contact conditions are used to identify which part of the slave surface is initially bonded, as explained earlier.

Boundary conditions should not be applied to any of the nodes on the master or slave crack surfaces, but they can be used to load the structure and cause crack propagation. In a low-cycle fatigue analysis, prescribed boundary conditions must have an amplitude definition that is cyclic over the step: the start value must be equal to the end value see Amplitude Curves.

Concentrated nodal forces can be applied to the displacement degrees of freedom 1—6 ; see Concentrated loads. Distributed pressure forces or body forces can be applied; see Distributed loads. The distributed load types available with particular elements are described in Abaqus Elements Guide.

For a low-cycle fatigue analysis each load must have an amplitude definition that is cyclic over the step: the start value must be equal to the end value see Amplitude Curves.

The following predefined fields can be specified in a crack propagation analysis, as described in Predefined Fields :. The specified temperature affects temperature-dependent critical stress and crack opening displacement failure criteria, if specified. The values of user-defined field variables can be specified.

These values affect field-variable-dependent critical stress and crack opening displacement failure criteria, if specified. The temperatures and user-defined field variables on slave and master surfaces are averaged to determine the critical stresses and crack opening displacements. In a low-cycle fatigue analysis, the temperature values specified must be cyclic over the step: the start value must be equal to the end value see Amplitude Curves.

Alternatively, you can ramp the temperatures back to their initial condition values, as described in Predefined Fields. See Abaqus Materials Guide. Regular, rectangular meshes give the best results in crack propagation analyses. Results with nonlinear materials are more sensitive to meshing than results with small-strain linear elasticity.

The VCCT , enhanced VCCT , and low-cycle fatigue criteria not only support two-dimensional models planar and axisymmetric but also three-dimensional models with contact pairs involving first-order underlying elements solids, shells, and continuum shells.

Use of the low-cycle fatigue criterion with contact pairs involving higher-order underlying elements is not supported. Unless otherwise stated, the following discussions in this section are applied only to the critical stress, critical crack opening displacement, and crack length versus time criteria. The initial contact status of all of the slave surface nodes is printed in the data. The slave and master surfaces that are associated with these cracks are also identified.

The initial contact status of all of the slave surface nodes is also printed in the data. By default, crack propagation information will be printed to the data file during the analysis. For example, if the crack opening displacement criterion is used, the printed output during the analysis will appear as follows in the data file:.

By default, the crack-tip location and associated quantities will be printed every increment. Specify an output frequency of 0 to suppress crack propagation output. The time when bond failure occurred.

Bond state. The bond state varies between 1. Surface output requests provide the usual output of contact variables in addition to the above quantities. The bond failure quantities must be requested explicitly; otherwise, only the default output for contact will be given. Contour integrals can be requested for two-dimensional crack propagation analyses performed using the critical stress, critical crack opening displacement, or crack length versus time fracture criteria.

If the contours are chosen so that the crack tip passes through the contour, the contour value will go to zero as it should. Therefore, in crack propagation analysis contour integrals should be requested far enough from the crack tip that the crack tip does not pass through the contour, which is easily done by including all nodes along the bond surface in the crack-tip node set specified. See Contour integral evaluation for details on contour integral output. By default, the nodes in the node set are considered to be initially bonded in all directions.

Bonding only in the normal direction For fracture criteria based on the critical stress, critical crack opening displacement, or crack length versus time, it is possible to bond the nodes in the node set or the contact pair if a node set is not defined only in the normal direction. Propagation of multiple cracks Cracks can propagate from either a single crack tip or multiple crack tips. Specifying a fracture criterion You can specify the crack propagation criteria, as discussed below.

Table 1. Figure 1. Distance specification for the critical stress criterion. Figure 2. Distance specification for the critical crack opening displacement criterion. Figure 3. Crack propagation as a function of time. Figure 4. Mode I: The energy released when a crack is extended by a certain amount is the same as the energy required to close the crack. Figure 5. Pure Mode I modified. Defining variable critical energy release rates You can define a VCCT criterion with varying energy release rates by specifying the critical energy release rates at the nodes.

Figure 6. Fatigue crack growth govern by Paris law. Onset of delamination growth The onset of delamination growth refers to the beginning of fatigue crack growth at the crack tip along the interface. Specifying a debonding amplitude curve When you use the critical stress, critical crack opening displacement, or crack length versus time fracture criteria, you can define how this force is to be reduced to zero with time after debonding starts at a particular node on the bonded surface.

Ramping down debonding force for the VCCT and the enhanced VCCT criteria For the VCCT and the enhanced VCCT criteria, when the energy release rate exceeds the critical value at a crack tip, you can either release the traction between the two surfaces at the crack tip immediately during the following increment or release the traction gradually during succeeding increments with the reduction of the magnitude of the debonding force being governed by the critical fracture energy release rate.

Procedures Crack propagation analysis can be performed for static or dynamic overloadings using the following procedures: Static stress analysis Quasi-static analysis Implicit dynamic analysis using direct integration Explicit dynamic analysis Fully coupled thermal-stress analysis It can also be performed for sub-critical cyclic fatigue loadings using the following procedure: Low-cycle fatigue analysis using the direct cyclic approach.

You must have continuous master debonding surfaces. Table 2. Comparing VCCT and cohesive elements. Simulation mechanics -driven crack propagation along a known crack surface. However, cohesive elements can also be placed between element faces as a mechanism for allowing individual elements to separate.

Models brittle fracture using LEFM only. Very general interaction modeling capability is possible. Uses a surface-based framework. Does not require additional elements. Require definition of the connectivity and interconnectivity of cohesive elements with the rest of the structure. For accuracy, the mesh of cohesive elements may need to be smaller than the surrounding structural mesh and the associated cohesive zone. As a result, cohesive elements may be more expensive. Requires a pre-existing flaw at the beginning of the crack surface.

Cannot model crack initiation from a surface that is not already cracked. Can model crack initiation from initially uncracked surfaces. The crack initiates when the cohesive traction stress exceeds a critical value. Crack propagates when strain energy release rate exceeds fracture toughness. Crack propagates according to cohesive damage model, usually calibrated so that the energy released when the crack is fully open equals the critical strain energy release rate.

Use the following option to specify the postfailure stress as a tabular function of the fracture energy:. The implementation of the stress-displacement concept in a finite element model requires the definition of a characteristic length associated with a material point. The characteristic crack length is based on the element geometry and formulation: it is a typical length of a line across an element for a first-order element; it is half of the same typical length for a second-order element.

For beams and trusses it is a characteristic length along the element axis. For membranes and shells it is a characteristic length in the reference surface. For axisymmetric elements it is a characteristic length in the r — z plane only. For cohesive elements it is equal to the constitutive thickness. We use this definition of the characteristic crack length because the direction in which cracks will occur is not known in advance.

Therefore, elements with large aspect ratios will have rather different behavior depending on the direction in which they crack: some mesh sensitivity remains because of this effect.

Elements that are as close to square as possible are, therefore, recommended unless you can predict the direction in which cracks will form. An important feature of the cracking model is that, whereas crack initiation is based on Mode I fracture only, postcracked behavior includes Mode II as well as Mode I.

The Mode II shear behavior is based on the common observation that the shear behavior depends on the amount of crack opening. More specifically, the cracked shear modulus is reduced as the crack opens. In these models the dependence is defined by expressing the postcracking shear modulus, G c , as a fraction of the uncracked shear modulus:. You can specify this dependence in piecewise linear form, as shown in Figure 4.

See A cracking model for concrete and other brittle materials for a discussion of how shear retention is calculated in the case of two or more cracks. Use the following option to specify the piecewise linear form of the shear retention model:. One experiment, a uniaxial tension test, is required to calibrate the simplest version of the brittle cracking model. Other experiments may be required to gain accuracy in postfailure behavior.

This test is difficult to perform because it is necessary to have a very stiff testing machine to record the postcracking response. Quite often such equipment is not available; in this situation you must make an assumption about the tensile failure strength of the material and the postcracking response. Uniaxial compression tests can be performed much more easily, so the compressive strength of concrete is usually known. The postcracking tensile response is highly dependent on the reinforcement present in the concrete.

In simulations of unreinforced concrete, the tension stiffening models that are based on fracture energy concepts should be utilized.

In simulations of reinforced concrete the stress-strain tension stiffening model should be used; the amount of tension stiffening depends on the reinforcement present, as discussed before. Calibration of the postcracking shear behavior requires combined tension and shear experiments, which are difficult to perform.

You can define brittle failure of the material. When one, two, or all three local direct cracking strain displacement components at a material point reach the value defined as the failure strain displacement , the material point fails and all the stress components are set to zero. If all of the material points in an element fail, the element is removed from the mesh.

For example, removal of a first-order reduced-integration solid element takes place as soon as its only integration point fails. However, all through-the-thickness integration points must fail before a shell element is removed from the mesh. If the postfailure relation is defined in terms of stress versus strain, the failure strain must be given as the failure criterion.

If the postfailure relation is defined in terms of stress versus displacement or stress versus fracture energy, the failure displacement must be given as the failure criterion. You can control how many cracks at a material point must fail before the material point is considered to have failed; the default is one crack.

The number of cracks that must fail can only be one for beam and truss elements; it cannot be greater than two for plane stress and shell elements; and it cannot be greater than three otherwise. The main motivation for including this capability is to help in computations where not removing an element that can no longer carry stress may lead to excessive distortion of that element and subsequent premature termination of the simulation.

For example, in a monotonically loaded structure whose failure mechanism is expected to be dominated by a single tensile macrofracture Mode I cracking , it may be reasonable to use the brittle failure criterion to remove elements. On the other hand, the fact that the brittle material loses its ability to carry tensile stress does not preclude it from withstanding compressive stress; therefore, it may not be appropriate to remove elements if the material is expected to carry compressive loads after it has failed in tension.

An example may be a shear wall subjected to cyclic loading as a result of some earthquake excitation; in this case cracks that develop completely under tensile stress will be able to carry compressive stress when load reversal takes place.

Thus, the effective use of the brittle failure criterion relies on you having some knowledge of the structural behavior and potential failure mechanism. The use of the brittle failure criterion based on an incorrect user assumption of the failure mechanism will generally result in an incorrect simulation. When you define brittle failure, you can control how many cracks must open to beyond the failure value before a material point is considered to have failed.

The default number of cracks one should be used for most structural applications where failure is dominated by Mode I type cracking. However, there are cases in which you should specify a higher number because multiple cracks need to form to develop the eventual failure mechanism. One example may be an unreinforced, deep concrete beam where the failure mechanism is dominated by shear; in this case it is possible that two cracks need to form at each material point for the shear failure mechanism to develop.

Again, the appropriate choice of the number of cracks that must fail relies on your knowledge of the structural and failure behaviors. It is possible to use the brittle failure criterion in brittle cracking elements for which rebar are also defined; the obvious application is the modeling of reinforced concrete.

When such elements fail according to the brittle failure criterion, the brittle cracking contribution to the element stress carrying capacity is removed but the rebar contribution to the element stress carrying capacity is not removed. However, if you also include shear failure in the rebar material definition, the rebar contribution to the element stress carrying capacity will also be removed if the shear failure criterion specified for the rebar is satisfied.

This allows the modeling of progressive failure of an under-reinforced concrete structure where the concrete fails first followed by ductile failure of the reinforcement. The model cannot be used with pipe and three-dimensional beam elements. Plane triangular, triangular prism, and tetrahedral elements are not recommended for use in reinforced concrete analysis since these elements do not support the use of rebar. Status of element brittle failure model.

The status of an element is 1. Reinforcement Reinforcement in concrete structures is typically provided by means of rebars. Crack detection A simple Rankine criterion is used to detect crack initiation. Tension stiffening You can specify the postfailure behavior for direct straining across cracks by means of a postfailure stress-strain relation or by applying a fracture energy cracking criterion.

Postfailure stress-strain relation In reinforced concrete the specification of postfailure behavior generally means giving the postfailure stress as a function of strain across the crack Figure 1. Figure 1. Postfailure stress-strain curve.