In this blog post I thought we would take a small dip into modeling fracture and failure with Abaqus. In conventional FEM methods for crack propagation, the initial crack location needs to be predefined. This is not necessary when using extended Finite Element Method (XFEM). XFEM uses enrichment terms to the normal displacement interpolation to describe the crack behavior.
Xfem Crack Propagation Abaqus Manual Pdf
Conventional fracture modeling only permits crack propagation along predefined boundaries. However, if we want to model bulk fracture and allow the crack to be located in the element interior, XFEM comes in handy.
The previous hip replacement geometry was used. This was then partitioned so that we could obtain a hexahedral mesh on the part. To accurately model the crack propagation path, a denser mesh would be needed for this part, but for illustration purposes, it should be enough.
To model crack propagation in Abaqus, we need to describe the damage initiation and evolution behaviors. For damage initiation, several criteria are available: maximum nominal stress/strain, quadratic nominal stress or maximum principal stress/strain. In each case, damage is assumed to initiate when the stress/strain satisfy the input damage criteria. In this case maximum principal stress (MAXPS damage) was used. This has the advantage that the crack plane can be perpendicular to the direction of maximum principal stress making it solution dependent. For this case, once the maximum principal stress exceed a value of 400 MPa.
The eXtended Finite Element Method (XFEM) is a versatile method for solving crack propagation problems. Meanwhile, XFEM predictions for crack onset and propagation rely on the stress field which tends to converge at a slower rate than that of displacements, making it challenging to capture critical load at crack onset accurately. Furthermore, identifying the critical region(s) for XFEM nodal enrichments is user-dependent. The identification process can be straightforward for small-scale test specimen while in other cases such as complex structures it can be unmanageable. In this work a novel approach is proposed with three major objectives; alleviate user-dependency; enhance predictions accuracy; minimize computational effort. An automatic critical region(s) identification based on material selected failure criterion is developed. Moreover, the approach enables the selection of optimized mesh necessary for accurate prediction of failure loads at crack initiation. Also, optimal enrichment zone size determination is automated. The proposed approach was developed as an iterative algorithm and implemented in ABAQUS using Python scripting. The proposed algorithm was validated against our test data of unnotched specimens and relevant test data from the literature. The results of the predicted loads/displacements at failure are in excellent agreement with measurements. Crack onset locations were in very good agreement with observations from testing. Finally, the proposed algorithm has shown a significant enhancement in the overall computational efficiency compared to the conventional XFEM. The proposed algorithm can be easily implemented into user-built or commercial finite element codes.
Therefore, in the current work, a novel approach is developed with the following objectives: (1) automatic identification of critical region(s) to alleviate user-dependency, (2) rigorous automatic mesh refinement based on stress convergence within these region(s) to ensure accurate predictions; and (3) automatically enriching critical region(s) for optimal XFEM execution. The main aim of current work is to eliminate the reliance on an expert user in identifying the critical region(s) and mesh refinement to enhance predictions accuracy at failure onset (damage initiation). For this purpose, an automation algorithm is developed to enable automatic identification of critical region(s) location/size and performing optimal mesh refinement procedure. The algorithm enriches only necessary nodes corresponding to the critical region(s) for XFEM modeling to predict the crack onset failure load and location. For the purpose of validating the current methodology, notched specimens were excluded since they are mainly used to study crack propagation rather than its onset. It is noteworthy to mention that the scope of the current work is predicting failure onset location together with failure loads/displacements with minimal user intervention to allow analyzing a real-life structure. To this end, a set of six unnotched concrete prismatic specimens were prepared and tested for validation. In addition further comparisons were established with relevant test data of unnotched specimens from the literature.
In the current work, some of XFEM implementation challenges are considered. The first challenge is the method dependency on user skills for critical region(s) identification for nodal enrichments. The second challenge stems from the high dependency of predictions accuracy on mesh quality and density. The proposed approach overcomes both challenges by automating the XFEM modeling process to arrive at a convergent mesh as well as potential (crack onset) zone without user intervention, hence allowing regular users to predict failure onset accurately. Another chief advantage of the proposed methodology is eliminating the need to embed initial cracks when analyzing crack propagation problems. This provides further advantages when the analysis is not limited to propagation and damage onset prediction is of primary importance. Critical load predictions at crack initiation facilitated by the current approach proved to be in excellent agreement with measurements obtained when testing unnotched specimens as well as relevant test data from the literature. Therefore, the proposed method allows accurate prediction of failure onset and eliminates the need for biasing specimens by introducing notches or first cracks. Furthermore, the proposed approach enables efficient mesh optimization and optimal enrichments which in turn enhances the overall computational efficiency. In conclusion, applying the proposed approach has significant effects on providing accurate and computationally efficient analysis of complex structures where critical region(s) identification can be challenging even for an expert user.
Throughout the domain of the problem, nodes which are not enriched by a Heaviside function nor a crack-tip asymptotic function are associated with the conventional shape functions of FEM. Hence, (1) can be simplified to include only the first summation term on RHS leading to the traditional formulation of FEM reading as For the region which is censored by the crack (crack domain), the displacement approximation function of XFEM can be reduced to only include both first and second summation terms of (1) and can be written asFinally, to account for the crack-tip singularities as well as its propagation, (1) can be reduced to only include first and third summation terms on the RHS which takes the form of (5) as follows:As can be observed from the previous equations, the computational effort required for the solution of XFEM is higher than that needed for conventional FEM, because XFEM accounts for more degrees of freedom to capture crack behavior using the same number of nodes leading to an increased problem size, demanding more computational effort.
There exist two approaches to analyze this problem using XFEM. The first approach is to embed an initial crack in the critical region to trigger crack propagation analysis as shown in Figure 4(a). Merely this is done to study crack propagation rather than its onset. Embedding initial cracks reduces the accuracy of predicted failure limits, which is detrimental in the case of brittle materials as their failure is said to be catastrophic; once the damage is initiated, it will rapidly propagate under various types of loading till fracture. In the second approach, the user is required to identify potential failure region(s) which might be a straightforward task for a small structure (e.g., specimen). On the other hand, it might become a very challenging task dealing with large structures. Upon identifying the critical region(s), the user would select this region(s) as shown in Figure 4(b). Corresponding nodes for this region(s) are enriched with XFEM unique shape functions to account for crack onset. Failing to identify the critical region(s) will potentially lead to the enrichment of the entire domain of the problem. Full domain enrichment results in a drastic increase of required computational requirements and there is a possibility of an ill-conditioned system of equations that may cause convergence problems. 2ff7e9595c
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