Modelling Crack Propagation Using XFEM Important

08/05/2017

Modelling crack propagation using XFEM

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Simuleon FEA Blog Modelling crack propagation using XFEM Posted by Dolf Broekaart on Mar 7, 2017 10:00:00 AM

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In a previous blog I showed how to model a stationary crack and calculate the Jintegral to determine whether the crack propagates. Abaqus offers different techniques to simulate crack propagation, including surface and elementbased cohesive behaviour and the virtual crack closure technique. When using one of these methods with conventional FEM, the location of the crack needs to be prescribed beforehand. When the eXtended Finite Element Method (XFEM) is used, this is not necessary. In this case, enrichment terms are added to the normal displacement interpolation, so a crack within an element can be described. In this blog I will explain how to model crack propagation using the surfacebased cohesive behaviour approach and XFEM. As an example, loading will be applied to a gear, similar to the stationary crack example. Only in this case, no crack will be present initially and it will develop based on the loading.

Meshing Meshing is much simpler, because it is not necessary to partition an initial crack or circular regions around the crack tip. Partitioning is only used to allow a finer mesh in the region where the crack will develop compared to the rest of the gear. http://info.simuleon.com/blog/modellingcrackpropagationusingxfem

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Linear brick elements are used (quadratic elements are not available for XFEM). Half of the gear is modelled, for reasons of symmetry.

Defining damage – damage initiation To model crack propagation in Abaqus both damage initiation and damage evolution need to be taken into account. Different criteria are available for damage initiation, in this case the maximum principal stress criterion will be used. Compared to criteria based on nominal stress or strain, using the principal stress or strain has the advantage that the crack plane can be perpendicular to the direction of the maximum principal stress, making it solution dependent. Damage initiation is defined as part of the material properties, using damage for Traction Separation laws => Maxps Damage. With this option, damage will initiate when the maximal principal stress exceeds the value given.

Defining damage – damage evolution By specifying damage initiation, you do not yet define how the material changes due to damage. Within Abaqus, damage is modelled using a scalar damage parameter, D. This can range between 0 (no damage) and 1 (complete failure). The stress that would have been there without damage is multiplied by (1 D) to calculate the stress including damage. Without damage (D=0) this leads to the undamaged response, with complete failure (D=1) the stress is 0 and in between a fraction of the stress will remain.

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In this example, damage is defined using a tractionseparation law and damage evolution is a suboption of Maxps Damage.

Either the maximal displacement or the fracture energy, which is the area under the curve in a graph of traction versus separation, must be specified. Different options are possible to specify the softening behaviour: how the tractionseparation graph goes from the point at the onset of damage to the completely failed state. In this case linear softening is used, corresponding to a straight line in the tractionseparation http://info.simuleon.com/blog/modellingcrackpropagationusingxfem

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graph. It is possible to take into account mode mixing, with the BK law, power law or tabularly specified data. Alternatively, modeindependent behaviour can be specified.

Defining damage damage stabilization Simulations including damage evolution often lead to convergence difficulties because of the softening in the material model. Abaqus allows the use of viscous regularization to stabilize the response during damage. For sufficiently small time steps, the tangent stiffness matrix will then be positive definite. A viscosity coefficient can be specified as a suboption of Maxps damage. It should be chosen in such a way that the influence of the stabilization on the final results is small. To check this, the output ALLVD (viscous dissipation) can be compared to ALLSE (strain energy). If ALLVD is not small compared to ALLSE, the viscous stabilization is likely influencing results. Playing around with the viscosity coefficient can help obtain a reasonable result within a reasonable amount of time.

Define crack Apart from defining when the material will damage and how it will behave after damage is initiated, the region where a crack can occur must be specified. This is the region where the enrichment terms will be added. Choosing Special => Crack => Create in the interaction module and selecting the type XFEM in the Create Crack dialog box that appears, allows you to select a crack domain. In this case, the cell where the crack will develop is chosen. http://info.simuleon.com/blog/modellingcrackpropagationusingxfem

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The ‘allow crack growth’ box should be checked, to allow the crack to propagate. XFEM can also be used for stationary cracks, allowing contour integrals such as the Jintegral to be calculated with less meshing effort. This is not discussed here. In this example, no initial crack is defined: it will develop based on the damage initiation criterion. If an initial crack is wanted, it is very easy to define with XFEM. A separate part representing the crack (without properties or mesh) can be instanced into the assembly and moved to the correct position. By choosing this part as crack location, the crack is defined. The crack does not need to be along the element edges. In fact, the XFEM method works best if the crack crosses through the element. Frictionless smallsliding contact can be defined for the contact between both sides of the crack.

Solution controls To aid in obtaining a converged solution, the solution controls can be modified. From the step module, select other => general solution controls => edit => step in which solution controls are to be edited. Press continue when a warning message is displayed. In the time incrementation tab, discontinuous analysis can be checked. This allows Abaqus to do more iterations before checking whether the solution is going anywhere. In the first More tab, the parameter I A can be increased from the default 5, to allow Abaqus more attempts before aborting the simulation. If large cutbacks are required, increasing the number of attempts is useful.


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Request output http://info.simuleon.com/blog/modellingcrackpropagationusingxfem

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For a simulation using XFEM, it is important to request PHILSM as output. This is the signed distance function to describe the crack surface using the level set method. If PHILSM is requested, Abaqus automatically creates an isosurface view cut based on this output, which shows the location of the crack. If it is not requested, the crack will not be visible and results shown will be counterintuitive. STATUSXFEM is also specific for XFEM. It gives the status of the enriched elements, it is 0.0 if the element is undamaged, 1.0 if the element is completely cut through (no traction forces remaining) and a value in between if the element is damaged but some traction forces remain. Of course the normal outputs such as stress and strain are available as well.

Results With the isosurface view cut based on PHILSM on (default) the results of this simulation nicely show the crack developing in time. By applying translucency, the internal part of the crack is also visible.

SIMULIA Abaqus - Fracture on gear using XF...

Are you interested to investigate if cracks will cause a potetial failure?

Talk to one of our FEA specialists today! Topics: Modelling crack propagation


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hamida fekirini 24/03/2017 à 00:14:01

Many thanks for this information I have a question what is the best, sketch a crack in the model or consider a crack as another part and in mode assembly we group the model with a crack Reply to hamida fekirini

Christine ObbinkHuizer 24/03/2017 à 14:47:05

It is best to create a separate part, instance it into the assembly at the appropriate position and refer to it in the crack definition. Apart from ease of meshing, this has the advantage that the crack will probably not be located at element edges, which is beneficial for the XFEM method. Reply to Christine ObbinkHuizer

Ricardo Dias 07/04/2017 à 18:15:53

Thanks for sharing this information! I have some questions regarding my work and I would be gratefull if you could give me some feedback: I'm doing a crack propagation on a three point bending test to extract the values of JIntegral and Factor Intensive Stress using XFEM. My goal is compared the results (JIntegral and FIS) between XFEM and Contour Integral Analysis. The simulation with Contour Integral analysis was carried out without any warning and I get my results. However, with the XFEM method I get warnings that I don't know how to solve, the warnings are: "Displacement increment for contact is too big." "There is zero FORCE everywhere in the model based on the default criterion. please check the value of the average FORCE during the current iteration to verify that the FORCE is small enough to be treated as zero. if not, please use the solution controls to reset the criterion for zero FORCE." http://info.simuleon.com/blog/modellingcrackpropagationusingxfem

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"The loading condition might make main crack under compression at nset 1. The crack propagation direction cannot be predicted. A value of zero is provided for it." I have been looking in the internet and wasn't able to find any reliable information about this. Best regards, Ricardo Dias Reply to Ricardo Dias

Christine Obbink Huizer 10/04/2017 à 08:44:13

It is impossible to really know what is going on without seeing the model, but my guess would be that there is something wrong in the model definition. For example, if the wrong side of a surface is defined in contact, this may result in strange behaviour. I recommend you to gradually build up the complexity of the model, so that it becomes clear what is causing these issues. Reply to Christine Obbink Huizer

Ricardo Dias 17/04/2017 à 12:34:23

Thanks for this information! I will follow your advice. Can you explain why you choose "discontinuous analysis" in general solution controls Step? For default this option is OFF. Should I turn ON? Best regards, Ricardo Dias Reply to Ricardo Dias

Christine Obbink Huizer 18/04/2017 à 08:57:31

Dear Ricardo, Abaqus uses Newton’s method to solve non linear equations. The ‘discontinuous analysis’ option increases I0 (the number of iterations after which the check is made that the residuals are not increasing in two consecutive iterations) and IR (the number of equilibrium iterations after http://info.simuleon.com/blog/modellingcrackpropagationusingxfem

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which the logarithmic rate of convergence check begins). So, with this setting more iterations are allowed before the solution needs to get closer each iteration. This can be beneficial for extremely nonlinear problems, such as those involving XFEM. The simulation may take longer, because it will continue to work on an increment that is too big longer. Apart from that, I do not expect negative effects, so it makes sense to try it for severely nonlinear problems.

Bensari Ahmed 21/04/2017 à 22:45:41

Hello, please i need help. i do a simulation of a fatigue crack propagation, my question is: how do i get the cuve lenght of crack vs number of cycle from odb data in abaqus. thanks in advance. Reply to Bensari Ahmed

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