Thank you for the thoughtful review of our recent paper. You bring up many different situations that might be encountered when a crack interacts with an interface. The methods developed in the paper seek to lay a foundation upon which we can incorporate more complicated scenarios, such as those you described above. For readers who have not viewed the paper, I will first provide some additional background information.
An important component of the framework involves a library of pre-created mesh patterns (referred to as templates) which are automatically inserted around the crack tip. The templates contain crack extension increments at many different angles, and they are incorporated into an existing FE model at a crack tip. The existing model can have up two 8 different material regions joining at the tip. For growth at each different angle of interest, there are two nearly identical templates, where the main difference is that in one of the templates the nodes along the extension increment are allowed to separate, while in the other template, the extension increment is simply represented in the mesh. These templates are automatically inserted and enable efficient acquisition of “before” and “after” FE analysis results. For the scenarios investigated in the current paper the GI and GII were obtained by considering the forces ahead of the crack tip in the “before” model and the corresponding opening displacements in the “after” model.
The situations you describe could be largely investigated by expanding the framework in two main areas: 1) extracting the criterion-specific stress/strain/displacement values from the FE results and 2) developing additional mesh template sets. First, thinking in terms of a fracture initiation criterion that requires a specific stress state or deformation, these values could be exported from the analysis results and automatically compared to the critical values. This would be a straightforward alteration to the existing code. To include a cohesive zone model, mesh template sets could be developed such that they included interface elements along the crack extension increment. The current implementation can use supplied interface toughness values that are dependent on the two adjacent materials. Different traction-separation relationships could likewise be applied depending on the combination of adjacent materials. Using the mesh templates to insert interface elements immediately ahead of the existing tip at any angle of interest, allows the crack to grow in any direction without having to follow a pre-determined path that contains interface elements. Additional work would be required to adjust the framework and existing FE code to properly handle the interface elements.
Overall, this methodology was developed to be expandable, so that it could be adapted to work with different fracture criteria and material properties. For any given multiple-material structure, appropriate criteria should be selected and incorporated into the framework when necessary.
Thank you for the thoughtful review of our recent paper. You bring up many different situations that might be encountered when a crack interacts with an interface. The methods developed in the paper seek to lay a foundation upon which we can incorporate more complicated scenarios, such as those you described above. For readers who have not viewed the paper, I will first provide some additional background information.
An important component of the framework involves a library of pre-created mesh patterns (referred to as templates) which are automatically inserted around the crack tip. The templates contain crack extension increments at many different angles, and they are incorporated into an existing FE model at a crack tip. The existing model can have up two 8 different material regions joining at the tip. For growth at each different angle of interest, there are two nearly identical templates, where the main difference is that in one of the templates the nodes along the extension increment are allowed to separate, while in the other template, the extension increment is simply represented in the mesh. These templates are automatically inserted and enable efficient acquisition of “before” and “after” FE analysis results. For the scenarios investigated in the current paper the GI and GII were obtained by considering the forces ahead of the crack tip in the “before” model and the corresponding opening displacements in the “after” model.
The situations you describe could be largely investigated by expanding the framework in two main areas: 1) extracting the criterion-specific stress/strain/displacement values from the FE results and 2) developing additional mesh template sets. First, thinking in terms of a fracture initiation criterion that requires a specific stress state or deformation, these values could be exported from the analysis results and automatically compared to the critical values. This would be a straightforward alteration to the existing code. To include a cohesive zone model, mesh template sets could be developed such that they included interface elements along the crack extension increment. The current implementation can use supplied interface toughness values that are dependent on the two adjacent materials. Different traction-separation relationships could likewise be applied depending on the combination of adjacent materials. Using the mesh templates to insert interface elements immediately ahead of the existing tip at any angle of interest, allows the crack to grow in any direction without having to follow a pre-determined path that contains interface elements. Additional work would be required to adjust the framework and existing FE code to properly handle the interface elements.
Overall, this methodology was developed to be expandable, so that it could be adapted to work with different fracture criteria and material properties. For any given multiple-material structure, appropriate criteria should be selected and incorporated into the framework when necessary.